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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : SWV884-1 : TPTP v9.3.1. Released v4.1.0.
% 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 : n013.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 09:00:54 AM UTC 2026

% Result   : Unsatisfiable 27.02s 7.35s
% Output   : Refutation 29.64s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      : 1107
% Syntax   : Number of formulae    : 2215 ( 453 unt;   0 typ;   0 def)
%            Number of atoms       : 5385 (1202 equ;   0 cnn)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives : 32220 (2968   ~;3170   |;   0   &;26082   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   9 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  112 ( 110 usr;  10 con; 0-5 aty)
%            Number of variables   : 6570 (   0   ^;6570   !;   0   ?;6570   :)

% Comments : 
%------------------------------------------------------------------------------
thf(c_Finite__Set_Ofinite_decl,type,
    c_Finite__Set_Ofinite: $i > $i > $o ).

thf(v_U_decl,type,
    v_U: $i ).

thf(tc_Com_Opname_decl,type,
    tc_Com_Opname: $i ).

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

thf(v_G_decl,type,
    v_G: $i ).

thf(c_Set_Oimage_decl,type,
    c_Set_Oimage: $i > $i > $i > $i > $i ).

thf(v_mgt__call_decl,type,
    v_mgt__call: $i ).

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

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

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

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

thf(v_na_decl,type,
    v_na: $i ).

thf(c_Finite__Set_Ocard_decl,type,
    c_Finite__Set_Ocard: $i > $i > $i ).

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

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

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

thf(v_pn_decl,type,
    v_pn: $i ).

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

thf(c_Set_Oinsert_decl,type,
    c_Set_Oinsert: $i > $i > $i > $i ).

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

thf(c_HOL_Oord__class_Oless_decl,type,
    c_HOL_Oord__class_Oless: $i > $i > $i > $o ).

thf(c_HOL_Otimes__class_Otimes_decl,type,
    c_HOL_Otimes__class_Otimes: $i > $i > $i > $i ).

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

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

thf(c_Ring__and__Field_Odvd__class_Odvd_decl,type,
    c_Ring__and__Field_Odvd__class_Odvd: $i > $i > $i > $o ).

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

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

thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
    c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).

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

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

thf(c_Nat_Osemiring__1__class_Oof__nat_decl,type,
    c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).

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

thf(class_Lattices_Olower__semilattice_decl,type,
    class_Lattices_Olower__semilattice: $i > $o ).

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

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

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

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

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

thf(class_Divides_Osemiring__div_decl,type,
    class_Divides_Osemiring__div: $i > $o ).

thf(c_Divides_Odiv__class_Omod_decl,type,
    c_Divides_Odiv__class_Omod: $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_Lattices_Obounded__lattice_decl,type,
    class_Lattices_Obounded__lattice: $i > $o ).

thf(c_Orderings_Obot__class_Obot_decl,type,
    c_Orderings_Obot__class_Obot: $i > $i ).

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

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

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

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

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

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

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

thf(class_Lattices_Olattice_decl,type,
    class_Lattices_Olattice: $i > $o ).

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

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

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

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

thf(class_Ring__and__Field_Oring__no__zero__divisors_decl,type,
    class_Ring__and__Field_Oring__no__zero__divisors: $i > $o ).

thf(class_Ring__and__Field_Odvd_decl,type,
    class_Ring__and__Field_Odvd: $i > $o ).

thf(c_Orderings_Otop__class_Otop_decl,type,
    c_Orderings_Otop__class_Otop: $i > $i ).

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

thf(class_Ring__and__Field_Oordered__semiring_decl,type,
    class_Ring__and__Field_Oordered__semiring: $i > $o ).

thf(class_OrderedGroup_Olordered__ab__group__add__meet_decl,type,
    class_OrderedGroup_Olordered__ab__group__add__meet: $i > $o ).

thf(class_Ring__and__Field_Omult__zero_decl,type,
    class_Ring__and__Field_Omult__zero: $i > $o ).

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

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

thf(class_Ring__and__Field_Ono__zero__divisors_decl,type,
    class_Ring__and__Field_Ono__zero__divisors: $i > $o ).

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

thf(c_SetInterval_Oord__class_OatLeast_decl,type,
    c_SetInterval_Oord__class_OatLeast: $i > $i > $i ).

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

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

thf(class_Ring__and__Field_Ozero__neq__one_decl,type,
    class_Ring__and__Field_Ozero__neq__one: $i > $o ).

thf(class_Nat_Osemiring__char__0_decl,type,
    class_Nat_Osemiring__char__0: $i > $o ).

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

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

thf(c_Fun_Ofun__upd_decl,type,
    c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).

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(class_Ring__and__Field_Omult__mono_decl,type,
    class_Ring__and__Field_Omult__mono: $i > $o ).

thf(class_Ring__and__Field_Omult__mono1_decl,type,
    class_Ring__and__Field_Omult__mono1: $i > $o ).

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

thf(class_Finite__Set_Ofinite_Ofinite_decl,type,
    class_Finite__Set_Ofinite_Ofinite: $i > $o ).

thf(c_Set_Ovimage_decl,type,
    c_Set_Ovimage: $i > $i > $i > $i > $i ).

thf(c_Fun_Oinj__on_decl,type,
    c_Fun_Oinj__on: $i > $i > $i > $i > $o ).

thf(class_Orderings_Obot_decl,type,
    class_Orderings_Obot: $i > $o ).

thf(c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1_decl,type,
    c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1: $i > $i > $i ).

thf(c_Hilbert__Choice_Oinv__into_decl,type,
    c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1_decl,type,
    c_ATP__Linkup_Osko__Set__Ximage__iff__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1_decl,type,
    c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1: $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1_decl,type,
    c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1_decl,type,
    c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1: $i > $i > $i > $i > $i > $i ).

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

thf(c_ATP__Linkup_Osko__Set__XimageE__1__1_decl,type,
    c_ATP__Linkup_Osko__Set__XimageE__1__1: $i > $i > $i > $i > $i > $i ).

thf(class_Orderings_Otop_decl,type,
    class_Orderings_Otop: $i > $o ).

thf(class_HOL_Oord_decl,type,
    class_HOL_Oord: $i > $o ).

thf(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1_decl,type,
    c_ATP__Linkup_Osko__Set__Ximage__cong__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1_decl,type,
    c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1: $i > $i ).

thf(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1_decl,type,
    c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_Finite__Set_Olinorder__class_OMax_decl,type,
    c_Finite__Set_Olinorder__class_OMax: $i > $i > $i ).

thf(c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1_decl,type,
    c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1: $i > $i > $i ).

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

thf(c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2_decl,type,
    c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2: $i > $i > $i > $i ).

thf(c_Inductive_Ocomplete__lattice__class_Ogfp_decl,type,
    c_Inductive_Ocomplete__lattice__class_Ogfp: $i > $i > $i ).

thf(class_Divides_Oring__div_decl,type,
    class_Divides_Oring__div: $i > $o ).

thf(c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2_decl,type,
    c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2: $i > $i > $i > $i ).

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

thf(c_Finite__Set_Olinorder__class_OMin_decl,type,
    c_Finite__Set_Olinorder__class_OMin: $i > $i > $i ).

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

thf(class_Complete__Lattice_Ocomplete__lattice_decl,type,
    class_Complete__Lattice_Ocomplete__lattice: $i > $o ).

thf(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1_decl,type,
    c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1: $i > $i > $i > $i > $i > $i ).

thf(c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1_decl,type,
    c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1: $i > $i ).

thf(c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1_decl,type,
    c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1: $i > $i ).

thf(750,axiom,
    tc_nat @ class_Nat_Osemiring__char__0,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

thf(2822,plain,
    tc_nat @ class_Nat_Osemiring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(650,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(2612,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(37,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).

thf(1190,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(984,axiom,
    tc_nat @ class_OrderedGroup_Omonoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

thf(3345,plain,
    tc_nat @ class_OrderedGroup_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).

thf(521,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).

thf(2336,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(371,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).

thf(1995,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(190,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

thf(1559,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(259,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).

thf(1729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(775,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).

thf(2876,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(1049,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_Inductive_Ocomplete__lattice__class_Ogfp ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gfp__upperbound_0) ).

thf(3477,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ hAPP ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_Inductive_Ocomplete__lattice__class_Ogfp ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).

thf(624,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__eq__diff__pred_0) ).

thf(2559,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(618,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).

thf(2544,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(1090,axiom,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

thf(3566,plain,
    tc_nat @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).

thf(483,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

thf(2250,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(459,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__left_0) ).

thf(2199,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(841,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).

thf(3021,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(92,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).

thf(1322,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(201,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).

thf(1586,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(166,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).

thf(1501,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(321,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_0) ).

thf(1879,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(99,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).

thf(1337,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(412,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

thf(2094,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(130,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).

thf(1411,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(222,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).

thf(1633,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(729,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).

thf(2778,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(1027,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__mod__geq_0) ).

thf(3434,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(906,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).

thf(3167,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(733,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).

thf(2787,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(309,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).

thf(1850,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(564,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

thf(2427,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(365,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

thf(1982,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

thf(1818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).

thf(1295,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(353,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

thf(1956,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(351,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1__is__0_0) ).

thf(1950,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(186,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel2_1) ).

thf(1549,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(497,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).

thf(2280,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(188,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_0) ).

thf(1554,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(6,negated_conjecture,
    ~ ( t_a @ ( v_G @ ( v_pn @ ( v_mgt__call @ hAPP ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).

thf(1110,plain,
    ~ ( t_a @ ( v_G @ ( v_pn @ ( v_mgt__call @ hAPP ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(909,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_1) ).

thf(3172,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(602,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).

thf(2512,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(79,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

thf(1290,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(215,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).

thf(1618,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(873,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).

thf(3098,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(678,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).

thf(2671,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(43,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Oone__class_Oone ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_1) ).

thf(1205,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Oone__class_Oone ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(71,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).

thf(1269,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(1060,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

thf(3498,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(533,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__card__mono_0) ).

thf(2363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(41,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

thf(1200,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(405,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__eq__0__iff_1) ).

thf(2077,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(128,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).

thf(1406,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(417,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

thf(2104,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(474,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).

thf(2231,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(654,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(2622,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(175,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B = D )
      | ( ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).

thf(1522,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B = D )
      | ( ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(665,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

thf(2644,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(594,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).

thf(2495,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(541,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inc__induct_2) ).

thf(2381,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( C @ ( A @ c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1 ) @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(547,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

thf(2395,plain,
    tc_nat @ class_Ring__and__Field_Osemiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(399,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

thf(2062,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(728,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

thf(2776,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ hAPP ) @ hBOOL )
      | ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(671,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).

thf(2659,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(1019,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) )
      | ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).

thf(3417,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) )
      | ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(849,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).

thf(3040,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(899,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( C @ ( B @ ( D @ c_in ) ) )
      | ( C @ ( A @ ( D @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).

thf(3153,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( C @ ( B @ ( D @ c_in ) ) )
      | ( C @ ( A @ ( D @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).

thf(1422,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(808,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).

thf(2947,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(194,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

thf(1569,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).

thf(1971,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(285,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).

thf(1793,plain,
    ! [A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(1012,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ( tc_nat @ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__le_0) ).

thf(3402,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ( tc_nat @ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).

thf(179,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__trans_0) ).

thf(1533,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(1073,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

thf(3530,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).

thf(236,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).

thf(1671,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(1030,axiom,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

thf(3439,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(230,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

thf(1655,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(883,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).

thf(3120,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(684,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).

thf(2686,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(995,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( E @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_1) ).

thf(3367,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( E @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(316,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).

thf(1867,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(803,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).

thf(2933,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(318,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

thf(1872,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(94,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__reduce_0) ).

thf(1327,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(762,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).

thf(2844,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(390,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).

thf(2042,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(435,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

thf(2146,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(169,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) )
       != ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__eq__iff_0) ).

thf(1507,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) )
       != ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(956,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).

thf(3276,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(457,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).

thf(2195,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(249,axiom,
    ! [A: $i] :
      ( A
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

thf(1705,plain,
    ! [A: $i] :
      ( A
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(709,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).

thf(2740,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(795,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).

thf(2918,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(26,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__eq_0) ).

thf(1164,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(1034,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__mono_0) ).

thf(3446,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(586,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).

thf(2476,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(656,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

thf(2627,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(368,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Oone__class_Oone ) )
      | ( ( tc_nat @ c_HOL_Oone__class_Oone )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_0) ).

thf(1988,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Oone__class_Oone ) )
      | ( ( tc_nat @ c_HOL_Oone__class_Oone )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(578,axiom,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).

thf(2459,plain,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(1018,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).

thf(3414,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(1051,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__eq__dividend_0) ).

thf(3481,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(980,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).

thf(3335,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).

thf(876,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) )
      | ~ ( E @ ( D @ ( C @ c_in ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).

thf(3103,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) )
      | ~ ( E @ ( D @ ( C @ c_in ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(467,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).

thf(2216,plain,
    tc_nat @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(392,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(2046,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(336,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1_0) ).

thf(1914,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(1062,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).

thf(3502,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
       != ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(197,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

thf(1576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(1066,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

thf(3513,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).

thf(870,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

thf(3088,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

thf(1613,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(339,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(1921,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(407,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).

thf(2082,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(604,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).

thf(2516,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(401,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

thf(2067,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(553,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1 ) ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_0) ).

thf(2405,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1 ) ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).

thf(1887,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(987,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Finite__Set_Olinorder__class_OMin ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).

thf(3350,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Finite__Set_Olinorder__class_OMin ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(701,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

thf(2723,plain,
    tc_nat @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).

thf(1127,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(722,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).

thf(2763,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(592,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).

thf(2491,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).

thf(1243,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(969,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).

thf(3308,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(377,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).

thf(2010,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(119,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).

thf(1386,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(959,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 ) ) ) ) @ ( A @ hAPP ) @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subsetI_1) ).

thf(3281,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 ) ) ) ) @ ( A @ hAPP ) @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(892,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(3140,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
     != ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(257,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).

thf(1724,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(447,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).

thf(2173,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(110,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).

thf(1366,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(1105,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).

thf(3597,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(1254,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(251,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).

thf(1709,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(845,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).

thf(3029,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

thf(1430,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(707,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).

thf(2735,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(389,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__right__eq_0) ).

thf(2039,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(675,axiom,
    tc_bool @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(2667,plain,
    tc_bool @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(983,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
      | ( A
        = ( A @ c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1 @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__D_0) ).

thf(3342,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
      | ( A
        = ( A @ c_ATP__Linkup_Osko__Nat__XSuc__le__D__1__1 @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).

thf(694,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__eq_0) ).

thf(2708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(597,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).

thf(2501,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(896,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(3148,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).

thf(494,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).

thf(2274,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(591,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).

thf(2488,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(988,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).

thf(3353,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

thf(711,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).

thf(2745,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(691,axiom,
    tc_bool @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(2703,plain,
    tc_bool @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(669,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).

thf(2654,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(1628,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(944,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( B @ c_in ) ) )
      | ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
        = ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).

thf(3248,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( F @ ( B @ c_in ) ) )
      | ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
        = ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(924,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff__eq__card_0) ).

thf(3204,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).

thf(1032,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).

thf(3442,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).

thf(78,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_0) ).

thf(1287,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(930,axiom,
    tc_nat @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(3221,plain,
    tc_nat @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(517,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).

thf(2328,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(794,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1__left_0) ).

thf(2916,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(232,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

thf(1660,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(271,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2__is__0_0) ).

thf(1760,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(888,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(3131,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(717,axiom,
    ! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__square_0) ).

thf(2755,plain,
    ! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(1059,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Ovimage ) ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).

thf(3495,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Ovimage ) ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(572,axiom,
    tc_bool @ class_Lattices_Obounded__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(2444,plain,
    tc_bool @ class_Lattices_Obounded__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(69,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(1264,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(468,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).

thf(2217,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(885,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).

thf(3125,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(300,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__reduce_1) ).

thf(1826,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(1080,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

thf(3542,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self2_0) ).

thf(1279,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(1016,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_lessequals ) ) )
      | ( C @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__inv__into_0) ).

thf(3410,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_lessequals ) ) )
      | ( C @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(452,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(2185,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(146,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib2_0) ).

thf(1455,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(582,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_1) ).

thf(2466,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(426,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

thf(2126,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(91,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).

thf(1319,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Otop__class_Otop @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(724,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

thf(2767,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(211,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).

thf(1609,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(195,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).

thf(1572,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(383,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).

thf(2024,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(544,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).

thf(2388,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(308,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult2_0) ).

thf(1847,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(755,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_0) ).

thf(2829,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(184,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).

thf(1545,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(560,axiom,
    tc_nat @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(2420,plain,
    tc_nat @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(998,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).

thf(3374,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(1003,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).

thf(3385,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(445,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

thf(2169,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(552,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).

thf(2403,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(172,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Oone__class_Oone ) )
      | ( ( tc_nat @ c_HOL_Oone__class_Oone )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_1) ).

thf(1514,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Oone__class_Oone ) )
      | ( ( tc_nat @ c_HOL_Oone__class_Oone )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(660,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).

thf(2635,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(1045,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_Suc__le__mono_0) ).

thf(3470,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)],[1045]) ).

thf(971,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).

thf(3312,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(344,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

thf(1931,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(838,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).

thf(3014,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(606,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(2520,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( B = D )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(506,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(2301,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(163,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(1494,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(828,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).

thf(2989,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(357,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

thf(1963,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(1107,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

thf(3602,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).

thf(319,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__distrib_0) ).

thf(1875,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(765,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image_0) ).

thf(2852,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(936,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__empty_0) ).

thf(3231,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).

thf(1232,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( D @ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(953,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).

thf(3268,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).

thf(949,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).

thf(3258,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(975,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).

thf(3322,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_0) ).

thf(1302,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self2_0) ).

thf(1714,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

thf(1450,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(410,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(2090,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).

thf(1373,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(731,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( E @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_1) ).

thf(2782,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( E @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(1,negated_conjecture,
    tc_Com_Opname @ ( v_U @ c_Finite__Set_Ofinite ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(1109,plain,
    tc_Com_Opname @ ( v_U @ c_Finite__Set_Ofinite ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(487,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_1) ).

thf(2259,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(904,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( A @ c_Finite__Set_Ocard ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__psubset_0) ).

thf(3163,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( A @ c_Finite__Set_Ocard ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).

thf(1072,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).

thf(3527,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).

thf(15,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).

thf(1136,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).

thf(1151,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(871,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

thf(3093,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).

thf(1581,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(898,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).

thf(3152,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(403,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

thf(2073,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(380,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).

thf(2017,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(577,axiom,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).

thf(2456,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(376,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = B )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__0_0) ).

thf(2007,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = B )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).

thf(1489,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(810,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).

thf(2950,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(1037,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).

thf(3453,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).

thf(476,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).

thf(2236,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(1029,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).

thf(3438,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).

thf(1071,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).

thf(3525,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).

thf(315,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = F )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).

thf(1864,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = F )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(301,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_0) ).

thf(1828,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(799,axiom,
    tc_nat @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

thf(2925,plain,
    tc_nat @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

thf(1978,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(1092,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).

thf(3569,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).

thf(238,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

thf(1677,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(616,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).

thf(2540,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(387,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(2034,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(600,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).

thf(2508,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(28,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

thf(1169,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(535,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).

thf(2367,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(757,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).

thf(2833,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( B @ hAPP ) @ c_Set_Oinsert ) ) @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(1021,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).

thf(3421,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(589,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) )
      | ( A
        = ( E @ ( D @ ( B @ ( A @ ( C @ c_ATP__Linkup_Osko__Set__XimageE__1__1 ) ) ) ) @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageE_0) ).

thf(2483,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) )
      | ( A
        = ( E @ ( D @ ( B @ ( A @ ( C @ c_ATP__Linkup_Osko__Set__XimageE__1__1 ) ) ) ) @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(1063,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).

thf(3505,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).

thf(431,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).

thf(2137,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

thf(1351,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(138,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

thf(1433,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(715,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ hAPP ) )
        = C )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
       != A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).

thf(2750,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( B @ ( A @ hAPP ) )
        = C )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
       != A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(207,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).

thf(1600,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(439,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

thf(2154,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(861,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).

thf(3068,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( tc_nat @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_1) ).

thf(1377,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( tc_nat @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) @ ( C @ hAPP ) @ hBOOL )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(607,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__add_1) ).

thf(2523,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(611,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).

thf(2530,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(217,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).

thf(1622,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(824,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).

thf(2979,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(123,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

thf(1394,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(901,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__iff_1) ).

thf(3157,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ ( B @ c_in ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(374,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).

thf(2002,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(942,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).

thf(3243,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(744,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

thf(2809,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(499,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).

thf(2286,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(662,axiom,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).

thf(2639,plain,
    ! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(933,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add1_0) ).

thf(3226,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(348,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).

thf(1943,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(741,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

thf(2804,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(817,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).

thf(2965,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(1057,axiom,
    tc_nat @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

thf(3492,plain,
    tc_nat @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).

thf(1014,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).

thf(3406,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(462,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_2) ).

thf(2205,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(246,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).

thf(1696,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(915,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).

thf(3184,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
      | ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(639,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).

thf(2586,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(825,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).

thf(2982,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(779,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).

thf(2884,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(362,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self1_0) ).

thf(1975,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(1065,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).

thf(3510,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).

thf(192,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_0) ).

thf(1564,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(721,axiom,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(2762,plain,
    tc_nat @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(1000,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

thf(3378,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).

thf(209,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

thf(1604,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(897,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).

thf(3151,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(837,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq2_0) ).

thf(3011,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(1102,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).

thf(3591,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ ( D @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).

thf(585,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( B @ ( A @ ( C @ c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 ) ) ) ) @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_2) ).

thf(2473,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( B @ ( A @ ( C @ c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 ) ) ) ) @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(632,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(2574,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Obot )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(666,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A @ ( B @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ c_in ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).

thf(2646,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A @ ( B @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ c_in ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(1074,axiom,
    tc_nat @ class_Divides_Osemiring__div,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Divides_Osemiring__div) ).

thf(3531,plain,
    tc_nat @ class_Divides_Osemiring__div,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).

thf(423,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__by__1_0) ).

thf(2118,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(153,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).

thf(1470,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(789,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(2905,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(848,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(3037,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(1098,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_full__nat__induct_1) ).

thf(3582,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1 @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).

thf(935,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__trans_0) ).

thf(3229,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(1036,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).

thf(3450,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).

thf(1040,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).

thf(3459,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(1091,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).

thf(3567,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

thf(1691,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(22,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

thf(1153,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(916,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(3186,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(280,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__mult_0) ).

thf(1783,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(708,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2 ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_3) ).

thf(2737,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2 ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(88,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

thf(1311,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(509,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(2307,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(854,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).

thf(3054,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(595,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).

thf(2496,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(734,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diff_0) ).

thf(2790,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(1083,axiom,
    tc_nat @ class_HOL_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).

thf(3550,plain,
    tc_nat @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

thf(373,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ ( B @ ( C @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self4_0) ).

thf(2000,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ ( B @ ( C @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(223,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__left__eq_0) ).

thf(1636,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(679,axiom,
    ( ( tc_nat @ c_HOL_Oone__class_Oone )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_One__nat__def_0) ).

thf(2673,plain,
    ( ( tc_nat @ c_HOL_Oone__class_Oone )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(640,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__antisym_0) ).

thf(2589,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(330,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).

thf(1900,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(950,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).

thf(3261,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(565,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).

thf(2428,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(482,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(2249,plain,
    tc_nat @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).

thf(1355,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_2) ).

thf(1123,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(30,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).

thf(1174,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(1217,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(234,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).

thf(1666,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(160,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__right_0) ).

thf(1487,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(890,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).

thf(3134,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( F = B )
      | ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
        = ( F @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(429,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

thf(2132,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(610,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__XimageE__1__1 ) ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageE_1) ).

thf(2528,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__XimageE__1__1 ) ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(961,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).

thf(3286,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(489,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).

thf(2264,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(555,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).

thf(2409,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(706,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).

thf(2733,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(101,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

thf(1343,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(174,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

thf(1519,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(643,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).

thf(2596,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(937,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).

thf(3233,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).

thf(997,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

thf(3371,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(299,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

thf(1824,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(437,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).

thf(2150,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(112,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

thf(1370,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(386,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).

thf(2032,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(827,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
      | ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).

thf(2986,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
      | ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(925,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).

thf(3207,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C @ ( B @ ( A @ c_in ) ) )
      | ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(548,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

thf(2396,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(57,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).

thf(1238,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).

thf(2015,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(813,axiom,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

thf(2958,plain,
    tc_nat @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(573,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).

thf(2445,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ hAPP ) @ hBOOL )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(208,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).

thf(1602,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(567,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).

thf(2433,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(627,axiom,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).

thf(2565,plain,
    tc_nat @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(218,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

thf(1624,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(45,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

thf(1210,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(525,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
      | ( tc_nat @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV__card__ge__0_0) ).

thf(2344,plain,
    ! [A: $i] :
      ( ~ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
      | ( tc_nat @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(918,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).

thf(3191,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
      | ( A = D )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).

thf(581,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

thf(2464,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(774,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).

thf(2873,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(673,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_1) ).

thf(2663,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(519,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__1_0) ).

thf(2332,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(753,axiom,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

thf(2826,plain,
    tc_nat @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(972,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_0) ).

thf(3314,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(749,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).

thf(2820,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(965,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( B @ c_in ) ) )
      | ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).

thf(3297,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( C @ ( B @ c_in ) ) )
      | ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(891,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).

thf(3137,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(860,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = A )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).

thf(3065,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = A )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(986,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semiring,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

thf(3349,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(1086,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).

thf(3556,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(1106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).

thf(3600,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).

thf(242,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

thf(1687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(147,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).

thf(1457,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(894,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

thf(3144,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Olattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

thf(24,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).

thf(1159,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(1077,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

thf(3535,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).

thf(304,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Oone__class_Oone ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__self__implies__10_0) ).

thf(1836,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Oone__class_Oone ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).

thf(1787,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

thf(1195,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(465,axiom,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
     != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).

thf(2211,plain,
    ! [A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
     != ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(122,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( A @ ( F @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Ring__and__Field_Odvd ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_0) ).

thf(1392,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( A @ ( F @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Ring__and__Field_Odvd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(473,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( A @ ( B @ c_in ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( A @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).

thf(2228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( A @ ( B @ c_in ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( A @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(1015,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
      | ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).

thf(3408,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
      | ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
      | ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(263,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

thf(1740,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = C )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(334,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__le__divisor_0) ).

thf(1910,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(1104,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).

thf(3595,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).

thf(725,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(2769,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(126,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).

thf(1402,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(480,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).

thf(2245,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(1044,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( A @ ( E @ c_in ) ) )
      | ( ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__f_0) ).

thf(3467,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( A @ ( E @ c_in ) ) )
      | ( ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(539,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).

thf(2377,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).

thf(1953,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(761,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__0__iff_0) ).

thf(2841,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(2,negated_conjecture,
    tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( tc_Com_Opname @ ( v_U @ ( v_mgt__call @ c_Set_Oimage ) ) ) @ ( v_G @ c_lessequals ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(1111,plain,
    tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( tc_Com_Opname @ ( v_U @ ( v_mgt__call @ c_Set_Oimage ) ) ) @ ( v_G @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(165,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).

thf(1498,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(875,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).

thf(3102,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(865,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).

thf(3078,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(939,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

thf(3237,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

thf(1118,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(596,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).

thf(2498,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(55,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

thf(1234,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(440,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__add_0) ).

thf(2157,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(422,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(2115,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(1052,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).

thf(3482,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).

thf(947,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(3254,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(415,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

thf(2100,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(275,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).

thf(1772,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

thf(1259,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(820,axiom,
    tc_nat @ class_Ring__and__Field_Ozero__neq__one,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

thf(2973,plain,
    tc_nat @ class_Ring__and__Field_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(531,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( C @ ( D @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).

thf(2359,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( C @ ( D @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).

thf(1375,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(929,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).

thf(3218,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).

thf(312,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(1856,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(182,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

thf(1540,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(1068,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__0__iff_2) ).

thf(3518,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(1004,axiom,
    tc_nat @ class_Ring__and__Field_Omult__zero,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

thf(3386,plain,
    tc_nat @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(703,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).

thf(2726,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(658,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).

thf(2631,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(702,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
      | ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).

thf(2724,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
      | ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(767,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).

thf(2858,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(614,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).

thf(2537,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(491,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).

thf(2268,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
    = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(1031,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).

thf(3440,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(858,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2 ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__SucD_3) ).

thf(3060,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2 ) ) )
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(911,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).

thf(3176,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(840,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( A @ c_Finite__Set_Ocard ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__singleton_0) ).

thf(3018,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( C @ ( A @ c_Finite__Set_Ocard ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(193,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).

thf(1567,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(95,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).

thf(1329,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(970,axiom,
    tc_bool @ class_HOL_Oord,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).

thf(3311,plain,
    tc_bool @ class_HOL_Oord,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(893,axiom,
    tc_bool @ class_Orderings_Otop,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).

thf(3143,plain,
    tc_bool @ class_Orderings_Otop,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(108,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).

thf(1361,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).

thf(1182,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

thf(1461,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(772,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).

thf(2868,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(200,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).

thf(1584,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(346,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B = D )
      | ( ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).

thf(1937,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B = D )
      | ( ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(419,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(2108,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(621,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ( tc_nat @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_2) ).

thf(2551,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ( tc_nat @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(667,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(2649,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(964,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__cong_0) ).

thf(3294,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(1094,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).

thf(3573,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__trivial_0) ).

thf(1419,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(579,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).

thf(2460,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(738,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).

thf(2798,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(240,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).

thf(1683,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(833,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

thf(3000,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(515,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).

thf(2323,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(912,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).

thf(3179,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ ( B @ ( C @ c_in ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).

thf(625,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).

thf(2561,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(926,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(3210,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).

thf(135,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).

thf(1424,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(511,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1 ) @ c_Suc @ ( B @ hAPP ) @ ( A @ ( B @ c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1 ) @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__Suc__mono__le_0) ).

thf(2312,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1 ) @ c_Suc @ ( B @ hAPP ) @ ( A @ ( B @ c_ATP__Linkup_Osko__Nat__Xorder__class__Xlift__Suc__mono__le__1__1 ) @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( B @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(131,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I4_J_0) ).

thf(1414,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(395,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).

thf(2053,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(1024,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).

thf(3428,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).

thf(292,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

thf(1810,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(284,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__self3_0) ).

thf(1791,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(47,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

thf(1214,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(919,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).

thf(3194,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(527,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) )
      | ( A
        = ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Set__Ximage__iff__1__1 ) ) ) ) @ ( B @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_1) ).

thf(2349,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_in ) ) )
      | ( A
        = ( E @ ( D @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Set__Ximage__iff__1__1 ) ) ) ) @ ( B @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(325,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

thf(1889,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(226,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__self_0) ).

thf(1644,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(277,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

thf(1776,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(644,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

thf(2598,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(235,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__times__mod__eq_0) ).

thf(1668,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(479,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

thf(2243,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(529,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1 ) @ c_Suc @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inc__induct_1) ).

thf(2355,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( C @ ( A @ c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1 ) @ c_Suc @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(366,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).

thf(1984,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(881,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = E )
      | ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_0) ).

thf(3115,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = E )
      | ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(979,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).

thf(3333,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(255,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

thf(1720,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(718,axiom,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).

thf(2756,plain,
    ! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(818,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).

thf(2968,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
      = ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(4,negated_conjecture,
    ( ( t_a @ ( v_G @ c_Finite__Set_Ocard ) )
    = ( tc_nat @ ( v_na @ c_Suc @ ( t_a @ ( t_a @ ( tc_Com_Opname @ ( v_U @ ( v_mgt__call @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).

thf(1114,plain,
    ( ( t_a @ ( v_G @ c_Finite__Set_Ocard ) )
    = ( tc_nat @ ( v_na @ c_Suc @ ( t_a @ ( t_a @ ( tc_Com_Opname @ ( v_U @ ( v_mgt__call @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(575,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).

thf(2450,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(1054,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( tc_nat @ ( C @ ( B @ c_Finite__Set_Ocard ) @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image__le_0) ).

thf(3486,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( tc_nat @ ( C @ ( B @ c_Finite__Set_Ocard ) @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

thf(202,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(1588,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(82,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

thf(1297,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(682,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_2) ).

thf(2681,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(178,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(1530,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(759,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diff__nat_0) ).

thf(2836,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(117,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

thf(1382,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(787,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).

thf(2900,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(302,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).

thf(1831,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(931,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).

thf(3222,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(1079,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( tc_nat @ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__le_0) ).

thf(3540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( tc_nat @ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).

thf(628,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).

thf(2566,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(288,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

thf(1799,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(310,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).

thf(1852,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(746,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
       != B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_0) ).

thf(2813,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
       != B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(689,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oantisym__conv_0) ).

thf(2697,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).

thf(1246,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(493,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).

thf(2272,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(993,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 ) ) ) ) @ ( A @ hAPP ) @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_2) ).

thf(3364,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( E @ ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 ) ) ) ) @ ( A @ hAPP ) @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).

thf(928,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).

thf(3215,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(176,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

thf(1525,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(714,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).

thf(2749,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(369,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).

thf(1991,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(800,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

thf(2926,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(461,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

thf(2203,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(294,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(1814,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(278,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).

thf(1779,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(464,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).

thf(2208,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(778,axiom,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_1) ).

thf(2883,plain,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(397,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

thf(2057,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(816,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).

thf(2963,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(151,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(1466,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(570,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) )
      | ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).

thf(2440,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) )
      | ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).

thf(1663,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(470,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(2221,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
       != ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(652,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).

thf(2617,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(562,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).

thf(2423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(791,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) )
      | ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).

thf(2909,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) )
      | ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(1048,axiom,
    tc_bool @ class_Finite__Set_Ofinite_Ofinite,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).

thf(3476,plain,
    tc_bool @ class_Finite__Set_Ofinite_Ofinite,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(97,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).

thf(1333,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(619,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) )
        = ( E @ ( D @ ( B @ ( C @ c_Set_Oimage ) ) ) ) )
      | ( ( E @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__cong__1__1 ) ) ) ) @ ( A @ hAPP ) )
       != ( E @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__cong__1__1 ) ) ) ) @ ( C @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__cong_1) ).

thf(2546,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) )
        = ( E @ ( D @ ( B @ ( C @ c_Set_Oimage ) ) ) ) )
      | ( ( E @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__cong__1__1 ) ) ) ) @ ( A @ hAPP ) )
       != ( E @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__cong__1__1 ) ) ) ) @ ( C @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(1089,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__1_0) ).

thf(3563,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).

thf(958,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__subset__iff_1) ).

thf(3279,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).

thf(1100,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).

thf(3587,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).

thf(914,axiom,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(3183,plain,
    ! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(1064,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).

thf(3508,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

thf(328,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_1) ).

thf(1895,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(27,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( E @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__dvd__mono_0) ).

thf(1167,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( E @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(454,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).

thf(2189,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(831,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).

thf(2995,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(170,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).

thf(1510,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(557,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).

thf(2413,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__right__eq_0) ).

thf(1680,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(990,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).

thf(3358,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(49,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

thf(1219,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(158,axiom,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
    = ( tc_nat @ c_HOL_Oone__class_Oone ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_2) ).

thf(1483,plain,
    ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
    = ( tc_nat @ c_HOL_Oone__class_Oone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(73,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

thf(1273,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult2_0) ).

thf(1927,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(962,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(3289,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(646,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__if_1) ).

thf(2602,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(784,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).

thf(2894,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(221,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

thf(1631,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(424,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).

thf(2121,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(434,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

thf(2144,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

thf(1146,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(269,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

thf(1754,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(502,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).

thf(2292,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(355,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(1959,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(623,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_1) ).

thf(2556,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(850,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ c_Suc @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).

thf(3042,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ c_Suc @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(638,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oeq__iff_0) ).

thf(2585,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(630,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

thf(2570,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(266,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).

thf(1747,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(806,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__diff_0) ).

thf(2941,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(205,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).

thf(1595,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(1070,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).

thf(3523,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).

thf(608,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).

thf(2524,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(1009,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_0) ).

thf(3396,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(1005,axiom,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Ring__and__Field_Odvd__class_Odvd ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__1__iff__1_1) ).

thf(3387,plain,
    tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Ring__and__Field_Odvd__class_Odvd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(862,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).

thf(3070,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(337,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
      = ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).

thf(1916,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
      = ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(323,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).

thf(1884,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = F )
      | ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
        = ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(214,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).

thf(1615,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).

thf(1125,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(670,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_Suc @ c_lessequals ) ) )
      | ~ ( C @ ( A @ c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1 ) @ c_Suc @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__D__lemma_1) ).

thf(2657,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_Suc @ c_lessequals ) ) )
      | ~ ( C @ ( A @ c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1 ) @ c_Suc @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).

thf(1388,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(286,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).

thf(1795,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(697,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).

thf(2716,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) )
      | ( ( B @ ( A @ hAPP ) )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(1013,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Ole__less__trans_0) ).

thf(3404,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(754,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).

thf(2827,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(814,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).

thf(2959,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(1082,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).

thf(3547,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).

thf(303,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

thf(1833,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(819,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(2970,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(974,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).

thf(3319,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(393,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

thf(2048,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(805,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( E @ c_lessequals ) ) )
      | ( ( C @ ( D @ ( D @ ( C @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__image__cancel_0) ).

thf(2938,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( E @ c_lessequals ) ) )
      | ( ( C @ ( D @ ( D @ ( C @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).

thf(1620,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(1046,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( B @ hAPP ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__f_0) ).

thf(3472,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( B @ hAPP ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(268,axiom,
    ( ( tc_nat @ c_HOL_Oone__class_Oone )
    = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__1__eq__mult__iff_2) ).

thf(1752,plain,
    ( ( tc_nat @ c_HOL_Oone__class_Oone )
    = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(546,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_Suc__le__mono_1) ).

thf(2393,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)],[546]) ).

thf(869,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).

thf(3086,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(1652,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(343,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

thf(1929,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(960,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( B = A )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Ole__neq__trans_0) ).

thf(3283,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( B = A )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(629,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( A @ c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1 @ ( A @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__induct__lemma_1) ).

thf(2568,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( A @ c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1 @ ( A @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(180,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

thf(1535,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(742,axiom,
    tc_nat @ class_Orderings_Obot,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

thf(2806,plain,
    tc_nat @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

thf(1226,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(688,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).

thf(2695,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(66,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

thf(1256,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(882,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).

thf(3118,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(385,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).

thf(2029,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(978,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

thf(3330,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(804,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(2935,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(982,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).

thf(3340,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
      | ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).

thf(884,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

thf(3123,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(396,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

thf(2055,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(1096,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).

thf(3579,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

thf(329,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).

thf(1897,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(563,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).

thf(2425,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

thf(1464,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(967,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

thf(3302,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(51,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).

thf(1224,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(907,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).

thf(3170,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(1075,axiom,
    tc_bool @ class_Orderings_Oorder,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(3532,plain,
    tc_bool @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).

thf(16,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__left_2) ).

thf(1139,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(167,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).

thf(1503,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(456,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel__right_1) ).

thf(2193,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(842,axiom,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).

thf(3023,plain,
    ! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(250,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_1) ).

thf(1707,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(853,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_1) ).

thf(3051,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(783,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( F @ c_in ) ) )
      | ( E = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
       != ( F @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__injective_0) ).

thf(2891,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) )
      | ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( F @ c_in ) ) )
      | ( E = F )
      | ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
       != ( F @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(72,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).

thf(1271,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(571,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).

thf(2442,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(716,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__le__trans_1) ).

thf(2753,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(436,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

thf(2148,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(513,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).

thf(2319,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(601,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).

thf(2510,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(526,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( tc_nat @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_1) ).

thf(2346,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( tc_nat @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(196,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

thf(1574,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(727,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).

thf(2774,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(1020,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1 @ ( C @ c_Suc @ c_lessequals ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_full__nat__induct_0) ).

thf(3419,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ c_ATP__Linkup_Osko__Nat__Xfull__nat__induct__1__1 @ ( C @ c_Suc @ c_lessequals ) ) )
      | ( C @ ( A @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(877,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).

thf(3106,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(921,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).

thf(3197,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(785,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).

thf(2896,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(400,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(2065,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(406,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

thf(2079,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(532,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(2361,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(615,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( C @ ( A @ c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1 ) @ c_HOL_Oord__class_Oless ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inc__induct_0) ).

thf(2538,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( C @ ( A @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( C @ ( A @ c_ATP__Linkup_Osko__Nat__Xinc__induct__1__1 ) @ c_HOL_Oord__class_Oless ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(129,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(1408,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(76,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).

thf(1282,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(945,axiom,
    tc_nat @ class_Lattices_Olattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(3251,plain,
    tc_nat @ class_Lattices_Olattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(664,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).

thf(2642,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(900,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

thf(3155,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(408,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).

thf(2084,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_Orderings_Otop__class_Otop ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
       != ( A @ c_Orderings_Otop__class_Otop ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(940,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_0) ).

thf(3238,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(466,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).

thf(2214,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(542,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).

thf(2383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(558,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).

thf(2415,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(593,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_0) ).

thf(2493,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( A @ ( tc_nat @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(661,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

thf(2637,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(1084,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Finite__Set_Olinorder__class_OMax ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).

thf(3551,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Finite__Set_Olinorder__class_OMax ) )
        = B )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).

thf(103,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).

thf(1349,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(954,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(3270,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(812,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( A @ ( C @ ( C @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__inv__f__f_0) ).

thf(2955,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( A @ ( C @ ( C @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(505,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).

thf(2299,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(256,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_0) ).

thf(1722,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(677,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).

thf(2669,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(18,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).

thf(1144,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(740,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).

thf(2802,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(1061,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) )
      | ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).

thf(3500,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) )
      | ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(773,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Otop )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).

thf(2871,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Otop )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(140,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__eq__mod__eq__0_1) ).

thf(1439,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(458,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).

thf(2197,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).

thf(1969,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(86,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Odvd ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvdI_0) ).

thf(1307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Odvd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(450,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

thf(2180,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(752,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

thf(2824,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(451,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).

thf(2182,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__meet ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(320,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

thf(1877,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(745,axiom,
    tc_nat @ class_Ring__and__Field_Omult__mono1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).

thf(2812,plain,
    tc_nat @ class_Ring__and__Field_Omult__mono1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(710,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).

thf(2742,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(863,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ hAPP ) @ ( E @ ( C @ ( D @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
        = A )
      | ~ ( E @ ( C @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__eq_0) ).

thf(3073,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ hAPP ) @ ( E @ ( C @ ( D @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
        = A )
      | ~ ( E @ ( C @ ( B @ ( D @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(370,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).

thf(1993,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(730,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).

thf(2780,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(260,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

thf(1731,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(25,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

thf(1162,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(719,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ ( B @ c_in ) ) )
      | ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
        = ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).

thf(2757,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( F @ ( B @ c_in ) ) )
      | ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
        = ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(835,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ ( F @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( B @ ( D @ ( C @ ( E @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( B @ ( D @ ( C @ ( E @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
        = ( D @ ( C @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).

thf(3006,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ ( F @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( B @ ( D @ ( C @ ( E @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( B @ ( D @ ( C @ ( E @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
        = ( D @ ( C @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(20,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(1149,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(617,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( E @ ( B @ c_in ) ) )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).

thf(2542,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( F @ ( E @ ( B @ c_in ) ) )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(484,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) )
        = ( tc_nat @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ocard ) @ ( C @ ( A @ c_Finite__Set_Ocard ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__subset__Int_0) ).

thf(2252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) )
        = ( tc_nat @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ocard ) @ ( C @ ( A @ c_Finite__Set_Ocard ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(821,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).

thf(2974,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(647,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).

thf(2605,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(649,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).

thf(2610,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(855,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__1__left_0) ).

thf(3055,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(189,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).

thf(1557,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(512,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

thf(2314,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( ( A @ c_Suc )
       != ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(655,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).

thf(2625,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(905,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).

thf(3165,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(314,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__dvd_0) ).

thf(1862,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(847,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).

thf(3034,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
       != ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(797,axiom,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).

thf(2923,plain,
    ! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(93,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(1325,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(80,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__right_0) ).

thf(1293,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(496,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).

thf(2278,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(801,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).

thf(2928,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(31,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

thf(1177,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(792,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).

thf(2911,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(297,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(1820,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(7,negated_conjecture,
    ~ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( tc_Com_Opname @ ( v_U @ ( v_mgt__call @ c_Set_Oimage ) ) ) @ ( t_a @ ( v_G @ ( v_pn @ ( v_mgt__call @ hAPP ) @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).

thf(1112,plain,
    ~ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( tc_Com_Opname @ ( v_U @ ( v_mgt__call @ c_Set_Oimage ) ) ) @ ( t_a @ ( v_G @ ( v_pn @ ( v_mgt__call @ hAPP ) @ c_Set_Oinsert ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(634,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

thf(2578,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(29,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(1171,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(404,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

thf(2075,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(534,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).

thf(2365,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(155,axiom,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

thf(1474,plain,
    ! [A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(446,axiom,
    ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

thf(2171,plain,
    ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(879,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).

thf(3110,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(432,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( C
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_0) ).

thf(2139,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( C
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(500,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(2288,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Lattices_Obounded__lattice )
      | ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(641,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).

thf(2592,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
      = C ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(463,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).

thf(2207,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(687,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( C @ hAPP ) @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ c_Inductive_Ocomplete__lattice__class_Ogfp ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__coinduct__image_0) ).

thf(2693,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( C @ hAPP ) @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ c_Inductive_Ocomplete__lattice__class_Ogfp ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

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

thf(2867,plain,
    tc_nat @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(40,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__imp__dvd_0) ).

thf(1198,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(306,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__mult1_0) ).

thf(1841,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(124,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I2_J_0) ).

thf(1396,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(551,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).

thf(2401,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Ovimage ) ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(247,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mod__eq__iff_1) ).

thf(1699,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(394,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).

thf(2051,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(723,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

thf(2765,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(1022,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).

thf(3423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).

thf(60,axiom,
    tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__1__iff__1_1) ).

thf(1245,plain,
    tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Ring__and__Field_Odvd__class_Odvd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(588,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).

thf(2481,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(653,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( D @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).

thf(2620,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( C @ ( A @ ( D @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(142,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).

thf(1445,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( A @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(177,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod__iff_1) ).

thf(1528,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(902,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).

thf(3159,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
      = ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(536,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( A
        = ( B @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).

thf(2369,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( A
        = ( B @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(941,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oorder__trans_0) ).

thf(3241,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(3,negated_conjecture,
    tc_nat @ ( t_a @ ( t_a @ ( tc_Com_Opname @ ( v_U @ ( v_mgt__call @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) @ ( v_na @ c_Suc @ c_lessequals ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(1113,plain,
    tc_nat @ ( t_a @ ( t_a @ ( tc_Com_Opname @ ( v_U @ ( v_mgt__call @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) @ ( v_na @ c_Suc @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(737,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).

thf(2797,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(839,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).

thf(3016,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(659,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).

thf(2633,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(382,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).

thf(2022,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(156,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).

thf(1477,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(976,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).

thf(3325,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).

thf(258,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

thf(1726,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(545,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).

thf(2390,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
        = ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(63,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

thf(1250,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(164,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_1) ).

thf(1496,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(507,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).

thf(2303,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(826,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).

thf(2984,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(361,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

thf(1973,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(290,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).

thf(1805,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(599,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).

thf(2506,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(1056,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).

thf(3490,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).

thf(1001,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMin ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).

thf(3380,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
      | ( C
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMin ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(350,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).

thf(1948,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(811,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).

thf(2952,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(85,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

thf(1304,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(732,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).

thf(2784,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
     != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(598,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ c_Finite__Set_Ocard ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) @ c_Suc ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_4) ).

thf(2503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( C @ ( B @ c_Finite__Set_Ocard ) )
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( B @ c_Finite__Set_Ocard ) @ c_Suc ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(895,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).

thf(3146,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(657,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).

thf(2629,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

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

thf(1340,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(187,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).

thf(1551,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(636,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).

thf(2582,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(219,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__1__right_0) ).

thf(1626,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(836,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).

thf(3009,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(1033,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).

thf(3444,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(477,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).

thf(2239,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(846,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) )
        = ( tc_nat @ ( C @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( A @ c_Finite__Set_Ocard ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__subset_0) ).

thf(3031,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) )
        = ( tc_nat @ ( C @ ( B @ c_Finite__Set_Ocard ) @ ( C @ ( A @ c_Finite__Set_Ocard ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(747,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_1) ).

thf(2816,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(651,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__1__iff__1_0) ).

thf(2614,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(413,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).

thf(2096,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(42,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

thf(1203,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(44,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

thf(1208,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(1095,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
        = B )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc_1) ).

thf(3576,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc )
        = B )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
        = ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).

thf(674,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).

thf(2665,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(903,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).

thf(3161,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(332,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__1_0) ).

thf(1905,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_nat @ c_HOL_Oone__class_Oone @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(852,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(3048,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
      | ( C = B )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(683,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).

thf(2684,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(1038,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).

thf(3455,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).

thf(154,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_2) ).

thf(1472,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(957,axiom,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).

thf(3278,plain,
    ! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(354,axiom,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel__disj_1) ).

thf(1958,plain,
    ! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(603,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).

thf(2513,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(185,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).

thf(1547,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(1007,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(3391,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = E )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).

thf(999,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).

thf(3376,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(769,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 ) ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_0) ).

thf(2863,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 ) ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(356,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).

thf(1961,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(549,axiom,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).

thf(2397,plain,
    ! [B: $i,A: $i] :
      ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(672,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( E @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_0) ).

thf(2661,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( E @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(867,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert_0) ).

thf(3082,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(378,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).

thf(2012,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(227,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).

thf(1647,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(64,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).

thf(1252,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(887,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(3129,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Oorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(699,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( B @ ( A @ ( C @ c_Fun_Oinj__on ) ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).

thf(2720,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( B @ ( A @ ( C @ c_Fun_Oinj__on ) ) ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(782,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).

thf(2888,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(756,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_5) ).

thf(2831,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(823,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).

thf(2977,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(212,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult_0) ).

thf(1611,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(23,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(1156,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(398,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).

thf(2060,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(264,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).

thf(1743,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(681,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).

thf(2678,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(605,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_lessequals ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).

thf(2518,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( D @ c_lessequals ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(111,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__dvd__cancel1_0) ).

thf(1368,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(448,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).

thf(2175,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(857,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).

thf(3058,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(554,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_2) ).

thf(2407,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(70,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

thf(1267,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(53,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).

thf(1230,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(764,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).

thf(2850,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(943,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).

thf(3246,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( F @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( E @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( F @ ( A @ ( E @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(1035,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( A @ c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1 @ c_Suc @ ( A @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__induct__lemma_0) ).

thf(3448,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( A @ hAPP ) @ hBOOL )
      | ( A @ c_ATP__Linkup_Osko__Nat__Xzero__induct__lemma__1__1 @ c_Suc @ ( A @ hAPP ) @ hBOOL )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).

thf(411,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).

thf(2092,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(471,axiom,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).

thf(2224,plain,
    ! [A: $i] :
      ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
      | ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(1085,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__1_0) ).

thf(3554,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).

thf(923,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff_0) ).

thf(3202,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(281,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__left_0) ).

thf(1785,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(522,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).

thf(2337,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( A @ ( B @ c_in ) ) )
      | ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(1081,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).

thf(3544,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

thf(1658,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(590,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

thf(2486,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(1017,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

thf(3412,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(13,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

thf(1130,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(583,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).

thf(2468,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(252,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

thf(1711,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(866,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) )
      | ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).

thf(3080,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) @ c_in ) ) )
      | ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(713,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(2747,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(968,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
     != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(3305,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
     != ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(443,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

thf(2165,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(685,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).

thf(2688,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(955,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ c_Suc )
        = B )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

thf(3273,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ c_Suc )
        = B )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(859,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).

thf(3063,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(796,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( C @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2 ) ) @ c_Finite__Set_Ocard ) )
        = C )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( C @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_2) ).

thf(2920,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( C @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xcard__Suc__eq__1__2 ) ) @ c_Finite__Set_Ocard ) )
        = C )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( C @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(36,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(1188,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(690,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).

thf(2700,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(35,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mod_0) ).

thf(1186,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( D @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(1047,axiom,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(3475,plain,
    tc_nat @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

thf(844,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).

thf(3026,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(495,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).

thf(2276,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(469,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).

thf(2219,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(364,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).

thf(1980,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(427,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

thf(2128,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(272,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

thf(1763,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(886,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).

thf(3127,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(910,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).

thf(3174,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(391,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(2044,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(345,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mod__cancel_0) ).

thf(1934,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(989,axiom,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).

thf(3356,plain,
    ! [A: $i] :
      ~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).

thf(635,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).

thf(2579,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(1006,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

thf(3388,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).

thf(948,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).

thf(3256,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(994,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).

thf(3366,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(490,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

thf(2266,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(58,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).

thf(1240,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(680,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(2675,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(127,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__lemma_0) ).

thf(1404,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( D @ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(107,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

thf(1358,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(481,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).

thf(2247,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(556,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).

thf(2411,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(1055,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).

thf(3488,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(183,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).

thf(1543,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(273,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__left__eq_0) ).

thf(1766,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(878,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_0) ).

thf(3107,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
      | ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(760,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).

thf(2838,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(421,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

thf(2113,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(17,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Suc @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).

thf(1141,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Suc @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(829,axiom,
    tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

thf(2992,plain,
    tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(289,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).

thf(1802,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(1058,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).

thf(3493,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(248,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).

thf(1702,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(540,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).

thf(2379,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
      | ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(50,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).

thf(1221,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(77,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

thf(1284,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(822,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

thf(2975,plain,
    ! [B: $i,A: $i] :
      ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(105,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).

thf(1353,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(530,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
      | ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 ) ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_1) ).

thf(2357,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
      | ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 ) ) ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(159,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

thf(1485,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(695,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).

thf(2711,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(267,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

thf(1749,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(932,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

thf(3224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(136,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

thf(1427,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(287,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

thf(1797,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(843,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).

thf(3024,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(768,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A @ ( B @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_in ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).

thf(2860,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A @ ( B @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_in ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(809,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).

thf(2949,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(700,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).

thf(2722,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(704,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( E @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq1_0) ).

thf(2728,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( D @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( E @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( tc_nat @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(254,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
       != ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
      | ~ ( A @ class_Nat_Osemiring__char__0 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

thf(1717,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
       != ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
      | ~ ( A @ class_Nat_Osemiring__char__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(322,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).

thf(1881,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Nat_Osemiring__1__class_Oof__nat ) )
        = ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(743,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).

thf(2807,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(637,axiom,
    tc_bool @ class_Orderings_Obot,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(2584,plain,
    tc_bool @ class_Orderings_Obot,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(1010,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).

thf(3398,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).

thf(587,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).

thf(2479,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ c_in ) ) )
      | ( D @ ( A @ ( B @ c_in ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(358,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).

thf(1966,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(908,axiom,
    tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

thf(3171,plain,
    tc_nat @ class_OrderedGroup_Opordered__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

thf(1076,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ ( C @ c_in ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__iff_0) ).

thf(3533,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ ( C @ c_in ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).

thf(917,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).

thf(3188,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
        = ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

thf(173,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

thf(1517,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(516,axiom,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_H_0) ).

thf(2325,plain,
    ! [A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).

thf(1781,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(5,negated_conjecture,
    tc_Com_Opname @ ( v_U @ ( v_pn @ c_in ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).

thf(1108,plain,
    tc_Com_Opname @ ( v_U @ ( v_pn @ c_in ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(770,axiom,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__eq__plus1_0) ).

thf(2865,plain,
    ! [A: $i] :
      ( ( A @ c_Suc )
      = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(347,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).

thf(1940,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(568,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).

thf(2435,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ ( A @ c_in ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(720,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__Suc__eq__Suc__mod_0) ).

thf(2760,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( A @ c_Suc @ c_Divides_Odiv__class_Omod ) ) )
      = ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_Suc @ c_Divides_Odiv__class_Omod ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(1011,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).

thf(3400,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(798,axiom,
    tc_bool @ class_Lattices_Olower__semilattice,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

thf(2924,plain,
    tc_bool @ class_Lattices_Olower__semilattice,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(305,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

thf(1839,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(1099,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ c_in ) ) )
      | ~ ( E @ ( D @ ( C @ c_in ) ) )
      | ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).

thf(3584,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( B @ c_in ) ) )
      | ~ ( E @ ( D @ ( C @ c_in ) ) )
      | ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).

thf(338,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

thf(1918,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(1039,axiom,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).

thf(3457,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(90,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Oone__class_Oone ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__1__iff_0) ).

thf(1316,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Oone__class_Oone ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(228,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zmod__simps_I1_J_0) ).

thf(1649,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( D @ ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(528,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

thf(2352,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(1101,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).

thf(3589,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).

thf(148,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).

thf(1459,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(748,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).

thf(2818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(32,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__dvd__not__less_0) ).

thf(1180,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(241,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(1685,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(780,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).

thf(2885,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(510,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(2310,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_Orderings_Opreorder )
      | ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(307,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = E )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

thf(1844,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = E )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(143,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).

thf(1448,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(453,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).

thf(2187,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(985,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oantisym_0) ).

thf(3346,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).

thf(420,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

thf(2110,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(121,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

thf(1390,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(508,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).

thf(2305,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ c_in ) ) )
      | ( D @ ( C @ ( A @ c_in ) ) )
      | ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(524,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) )
      | ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__into_0) ).

thf(2342,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) )
      | ( C @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(856,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

thf(3056,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(472,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(2226,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ hAPP ) @ hBOOL )
      | ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).

thf(1453,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

thf(1734,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(735,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).

thf(2792,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(291,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

thf(1807,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(790,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diffD_0) ).

thf(2907,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(372,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).

thf(1998,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
      = ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(1103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__subset__iff_0) ).

thf(3593,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).

thf(693,axiom,
    tc_nat @ class_Ring__and__Field_Odvd,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Odvd) ).

thf(2707,plain,
    tc_nat @ class_Ring__and__Field_Odvd,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(642,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).

thf(2594,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(444,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).

thf(2167,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(498,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

thf(2283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(501,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono1_0) ).

thf(2290,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(430,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).

thf(2135,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(622,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono_0) ).

thf(2554,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(612,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).

thf(2532,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(1002,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).

thf(3383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(375,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__eq_0) ).

thf(2004,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(265,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).

thf(1745,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(384,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

thf(2026,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(311,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).

thf(1854,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(946,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).

thf(3252,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_in ) ) )
      | ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(609,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).

thf(2526,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ class_HOL_Oord )
      | ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(868,axiom,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(3085,plain,
    tc_nat @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(1043,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__trans_1) ).

thf(3465,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(74,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

thf(1276,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(203,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( C = D )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).

thf(1590,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( C = D )
      | ( ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( tc_nat @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(414,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).

thf(2098,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(1053,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( E @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_0) ).

thf(3484,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( E @ ( tc_nat @ ( D @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).

thf(237,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

thf(1674,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(766,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
       != ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).

thf(2855,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
       != ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(1639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(996,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).

thf(3369,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

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

thf(2823,plain,
    tc_nat @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(648,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

thf(2608,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(938,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).

thf(3235,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(834,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).

thf(3003,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(298,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).

thf(1822,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(1067,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).

thf(3516,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).

thf(428,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__le_0) ).

thf(2130,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(438,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).

thf(2152,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(488,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).

thf(2262,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).

thf(1491,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(243,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).

thf(1689,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(913,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).

thf(3181,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(550,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( C @ ( B @ ( D @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).

thf(2399,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( C @ ( B @ ( D @ c_in ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(1025,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).

thf(3430,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(518,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).

thf(2330,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(633,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 ) ) ) ) @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subsetI_0) ).

thf(2576,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 ) ) ) ) @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(38,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(1193,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(442,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

thf(2162,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

thf(1212,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(788,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( B @ c_Finite__Set_Ocard ) @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__seteq_0) ).

thf(2902,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( B @ c_Finite__Set_Ocard ) @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(141,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__0_0) ).

thf(1442,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(381,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__0__left_0) ).

thf(2019,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(561,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).

thf(2421,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(574,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).

thf(2447,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
        = ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(807,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( D @ ( C @ ( B @ c_in ) ) )
      | ( ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__insert_0) ).

thf(2944,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( D @ ( C @ ( B @ c_in ) ) )
      | ( ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) )
        = ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(952,axiom,
    tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

thf(3267,plain,
    tc_nat @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).

thf(580,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono2_0) ).

thf(2462,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(388,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__self1_0) ).

thf(2036,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( B @ ( C @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(87,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

thf(1309,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(327,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).

thf(1893,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(503,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).

thf(2294,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ( A
        = ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(538,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) )
      | ( ( E @ ( D @ ( C @ ( A @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__inv__into__f_0) ).

thf(2374,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ c_in ) ) )
      | ( ( E @ ( D @ ( C @ ( A @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(198,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

thf(1578,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(543,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_Suc )
        = ( C @ ( A @ c_Finite__Set_Ocard ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__Diff1_0) ).

thf(2385,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_Suc )
        = ( C @ ( A @ c_Finite__Set_Ocard ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(963,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).

thf(3291,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
      | ( B
        = ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
      | ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
      | ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(698,axiom,
    tc_nat @ class_Ring__and__Field_Omult__mono,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).

thf(2719,plain,
    tc_nat @ class_Ring__and__Field_Omult__mono,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(475,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).

thf(2233,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
        = ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(951,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__left__eq_0) ).

thf(3264,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( A @ ( D @ ( B @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(874,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).

thf(3100,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(1069,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).

thf(3521,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).

thf(367,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).

thf(1986,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(981,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

thf(3337,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(270,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__if_0) ).

thf(1757,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(157,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

thf(1480,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(333,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).

thf(1908,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(433,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).

thf(2142,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(802,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(2930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(425,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

thf(2123,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(486,axiom,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(2258,plain,
    tc_nat @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

thf(1133,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(225,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

thf(1642,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(416,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).

thf(2102,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(171,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).

thf(1512,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(276,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

thf(1774,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(613,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( B = A )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oless__le_0) ).

thf(2534,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( B = A )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(485,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( B = C )
      | ~ ( E @ ( D @ ( B @ c_in ) ) )
      | ~ ( E @ ( D @ ( C @ c_in ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).

thf(2255,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ( B = C )
      | ~ ( E @ ( D @ ( B @ c_in ) ) )
      | ~ ( E @ ( D @ ( C @ c_in ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(204,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).

thf(1593,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(1042,axiom,
    ! [A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__cube_0) ).

thf(3464,plain,
    ! [A: $i] : ( tc_nat @ ( tc_nat @ ( tc_nat @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

thf(1380,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(889,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).

thf(3132,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(62,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__refl_0) ).

thf(1248,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(739,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

thf(2800,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
      = ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(977,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( A @ c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1 ) @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__D__lemma_0) ).

thf(3328,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_Suc @ c_lessequals ) ) )
      | ( tc_nat @ ( C @ ( A @ c_Natural_Osko__Natural__XSuc__le__D__lemma__1__1 ) @ ( C @ c_lessequals ) ) )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(460,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( A @ ( F @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Ring__and__Field_Odvd ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__period_I4_J_1) ).

thf(2201,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( A @ ( F @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring )
      | ~ ( A @ class_Ring__and__Field_Odvd ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(295,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).

thf(1816,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(1087,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).

thf(3558,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).

thf(712,axiom,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).

thf(2746,plain,
    ! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(283,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).

thf(1789,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(815,axiom,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).

thf(2961,plain,
    ( ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc )
    = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(793,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( B @ ( A @ ( C @ c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1 ) ) ) ) @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_1) ).

thf(2913,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
      | ( A
        = ( E @ ( D @ ( E @ ( D @ ( B @ ( A @ ( C @ c_ATP__Linkup_Osko__Set__Xsubset__image__iff__1__1 ) ) ) ) @ ( B @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(736,axiom,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mod_0) ).

thf(2795,plain,
    ! [B: $i,A: $i] :
      ( ( B @ ( A @ hAPP ) @ hBOOL )
      | ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Omod ) ) @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(851,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

thf(3045,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(102,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
        = ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__if_1) ).

thf(1346,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
        = ( tc_nat @ ( tc_nat @ ( B @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(668,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).

thf(2651,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(620,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__diffD1_0) ).

thf(2549,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( C @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(139,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__add__cong_0) ).

thf(1436,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Oplus__class_Oplus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(313,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).

thf(1859,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(109,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

thf(1363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(89,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(1314,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(520,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).

thf(2334,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(1088,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( A @ ( C @ ( C @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
        = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).

thf(3560,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
      | ( ( A @ ( C @ ( C @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
        = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).

thf(98,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

thf(1335,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(245,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).

thf(1693,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(402,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(2070,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(631,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).

thf(2572,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(191,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

thf(1561,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
      | ( A
       != ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(692,axiom,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(2704,plain,
    ! [A: $i] :
      ( A
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(1050,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

thf(3479,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(559,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

thf(2417,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) )
       != ( tc_nat @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(696,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_1) ).

thf(2714,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( D @ ( A @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( tc_nat @ ( A @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( E @ ( tc_nat @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(920,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).

thf(3196,plain,
    ! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(1023,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).

thf(3426,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
      | ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

thf(326,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).

thf(1891,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(523,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).

thf(2340,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(676,axiom,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).

thf(2668,plain,
    ! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(68,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

thf(1261,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(566,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).

thf(2430,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_nat @ ( A @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(763,axiom,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd_Oneq__le__trans_0) ).

thf(2847,plain,
    ! [B: $i,A: $i] :
      ( ( B = A )
      | ~ ( tc_nat @ ( A @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(991,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).

thf(3360,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( D @ ( C @ ( B @ c_in ) ) )
      | ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

thf(340,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(1923,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(206,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__mult__cong_0) ).

thf(1597,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( F @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( E @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( F @ c_Divides_Odiv__class_Omod ) ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
       != ( A @ ( C @ ( D @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(83,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

thf(1299,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(1120,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(537,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).

thf(2372,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
      | ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(56,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel_0) ).

thf(1236,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( C @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_Ring__and__Field_Odvd__class_Odvd ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(478,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) )
      | ( tc_nat @ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff2__less_0) ).

thf(2241,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ~ ( C @ ( A @ ( D @ c_in ) ) )
      | ( tc_nat @ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(441,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

thf(2159,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(992,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).

thf(3362,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).

thf(705,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

thf(2731,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(645,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__Ximage__iff__1__1 ) ) ) ) @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_0) ).

thf(2600,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( E @ ( E @ ( D @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( C @ c_in ) ) )
      | ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__Ximage__iff__1__1 ) ) ) ) @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(786,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).

thf(2898,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(1093,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__diff__right__eq_0) ).

thf(3570,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( C @ c_Divides_Odiv__class_Omod ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_Divides_Odiv__class_Omod ) ) ) )
      | ~ ( A @ class_Divides_Oring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).

thf(118,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).

thf(1384,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(181,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).

thf(1537,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(1078,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ ( E @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ ( E @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( tc_nat @ ( D @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__inj__on__le_0) ).

thf(3538,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( D @ ( B @ ( A @ ( E @ c_Fun_Oinj__on ) ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ ( E @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
      | ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
      | ( tc_nat @ ( D @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).

thf(341,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mod__less__divisor_0) ).

thf(1925,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Divides_Odiv__class_Omod ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(864,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).

thf(3076,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
      | ~ ( B @ ( C @ hAPP ) @ hBOOL )
      | ( B @ ( A @ hAPP ) @ hBOOL ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(880,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 ) ) ) ) @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_1) ).

thf(3113,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ ( C @ ( A @ ( E @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 ) ) ) ) @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(331,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__imp__mod__0_0) ).

thf(1902,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( ( A @ ( C @ ( B @ c_Divides_Odiv__class_Omod ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(1008,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_1) ).

thf(3394,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).

thf(168,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).

thf(1505,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).

thf(1399,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(492,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).

thf(2270,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( D @ ( A @ ( B @ c_in ) ) )
      | ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(1028,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).

thf(3437,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(1026,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

thf(3432,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(274,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Otop__class_Otop @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).

thf(1769,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_Orderings_Otop__class_Otop @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = B )
      | ~ ( A @ class_Lattices_Obounded__lattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(576,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).

thf(2453,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(335,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).

thf(1912,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( A @ ( D @ ( A @ ( C @ ( A @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( F @ ( A @ ( C @ ( E @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(449,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).

thf(2177,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(96,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(1331,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(210,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).

thf(1606,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(776,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).

thf(2879,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(663,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

thf(2640,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( C @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(1097,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_2) ).

thf(3580,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).

thf(1041,axiom,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).

thf(3461,plain,
    ! [A: $i] :
      ( ( tc_nat @ c_HOL_Ozero__class_Ozero )
     != ( A @ c_Suc ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(514,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).

thf(2321,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) @ ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(934,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).

thf(3227,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(626,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).

thf(2563,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(777,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).

thf(2881,plain,
    ! [B: $i,A: $i] :
      ( ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
      = ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(349,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel2_0) ).

thf(1945,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ( A
        = ( tc_nat @ c_HOL_Oone__class_Oone ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(927,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(3212,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( A = D )
      | ( A = E )
      | ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
       != ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(966,axiom,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) @ c_Suc ) )
      | ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Suc__eq_5) ).

thf(3299,plain,
    ! [B: $i,A: $i] :
      ( ( ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
        = ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) @ c_Suc ) )
      | ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(872,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).

thf(3096,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ( C @ ( B @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(262,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(1737,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(781,axiom,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

thf(2887,plain,
    ! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(34,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).

thf(1184,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(686,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( C @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2 ) ) @ c_Finite__Set_Ocard ) )
        = C )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( C @ c_Suc ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__SucD_2) ).

thf(2690,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( B @ ( B @ ( C @ ( A @ c_ATP__Linkup_Osko__Finite__Set__Xcard__eq__SucD__1__2 ) ) @ c_Finite__Set_Ocard ) )
        = C )
      | ( ( B @ ( A @ c_Finite__Set_Ocard ) )
       != ( C @ c_Suc ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(832,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).

thf(2998,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
      | ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(569,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).

thf(2438,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
      | ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(504,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( tc_nat @ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__less_0) ).

thf(2297,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
      | ~ ( C @ ( A @ ( B @ c_in ) ) )
      | ( tc_nat @ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(973,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) )
      | ~ ( E @ ( D @ ( C @ c_in ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).

thf(3316,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
      | ~ ( E @ ( D @ ( B @ c_in ) ) )
      | ~ ( E @ ( D @ ( C @ c_in ) ) )
      | ( ( B @ ( A @ hAPP ) )
       != ( C @ ( A @ hAPP ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(758,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).

thf(2834,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_nat @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(830,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).

thf(2993,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) )
      | ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(922,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ hAPP ) @ ( D @ c_lessequals ) ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Inductive_Ocomplete__lattice__class_Ogfp ) @ ( A @ c_in ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__coinduct_0) ).

thf(3200,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( C @ ( D @ ( A @ c_in ) ) )
      | ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ hAPP ) @ ( D @ c_lessequals ) ) )
      | ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Inductive_Ocomplete__lattice__class_Ogfp ) @ ( A @ c_in ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

thf(455,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).

thf(2191,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Lattices_Olower__semilattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(293,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__triv__right_0) ).

thf(1812,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(418,axiom,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dvd__mult__cancel1_1) ).

thf(2106,plain,
    ! [A: $i] :
      ( ( tc_nat @ ( A @ ( tc_nat @ ( tc_nat @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_Ring__and__Field_Odvd__class_Odvd ) ) )
      | ~ ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(409,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

thf(2087,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
        = ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
      | ~ ( A @ class_Lattices_Olattice ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(152,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

thf(1468,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(584,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
        = D )
      | ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__eq_0) ).

thf(2470,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( D @ ( A @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
        = D )
      | ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(132,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).

thf(1417,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( tc_nat @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(317,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

thf(1870,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_nat @ ( tc_nat @ ( A @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( B @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(726,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ ( C @ ( E @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__cong__1__1 ) ) ) ) @ c_in ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
        = ( D @ ( C @ ( B @ ( E @ c_Set_Oimage ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__cong_0) ).

thf(2771,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C @ ( B @ ( D @ ( C @ ( E @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__Ximage__cong__1__1 ) ) ) ) @ c_in ) ) )
      | ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
        = ( D @ ( C @ ( B @ ( E @ c_Set_Oimage ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(4214,plain,
    $false,
    inference(e,[status(thm)],[2822,2612,1190,3345,2336,1995,1559,1729,2876,3477,2559,2544,3566,2250,2199,3021,1322,1586,1501,1879,1337,2094,1411,1633,2778,3434,3167,2787,1850,2427,1982,1818,1295,1956,1950,1549,2280,1554,1110,3172,2512,1290,1618,3098,2671,1205,1269,3498,2363,1200,2077,1406,2104,2231,2622,1522,2644,2495,2381,2395,2062,2776,2659,3417,3040,3153,1422,2947,1569,1971,1793,3402,1533,3530,1671,3439,1655,3120,2686,3367,1867,2933,1872,1327,2844,2042,2146,1507,3276,2195,1705,2740,2918,1164,3446,2476,2627,1988,2459,3414,3481,3335,3103,2216,2046,1914,3502,1576,3513,3088,1613,1921,2082,2516,2067,2405,1887,3350,2723,1127,2763,2491,1243,3308,2010,1386,3281,3140,1724,2173,1366,3597,1254,1709,3029,1430,2735,2039,2667,3342,2708,2501,3148,2274,2488,3353,2745,2703,2654,1628,3248,3204,3442,1287,3221,2328,2916,1660,1760,3131,2755,3495,2444,1264,2217,3125,1826,3542,1279,3410,2185,1455,2466,2126,1319,2767,1609,1572,2024,2388,1847,2829,1545,2420,3374,3385,2169,2403,1514,2635,3470,3312,1931,3014,2520,2301,1494,2989,1963,3602,1875,2852,3231,1232,3268,3258,3322,1302,1714,1450,2090,1373,2782,1109,2259,3163,3527,1136,1151,3093,1581,3152,2073,2017,2456,2007,1489,2950,3453,2236,3438,3525,1864,1828,2925,1978,3569,1677,2540,2034,2508,1169,2367,2833,3421,2483,3505,2137,1351,1433,2750,1600,2154,3068,1377,2523,2530,1622,2979,1394,3157,2002,3243,2809,2286,2639,3226,1943,2804,2965,3492,3406,2205,1696,3184,2586,2982,2884,1975,3510,1564,2762,3378,1604,3151,3011,3591,2473,2574,2646,3531,2118,1470,2905,3037,3582,3229,3450,3459,3567,1691,1153,3186,1783,2737,1311,2307,3054,2496,2790,3550,2000,1636,2673,2589,1900,3261,2428,2249,1355,1123,1174,1217,1666,1487,3134,2132,2528,3286,2264,2409,2733,1343,1519,2596,3233,3371,1824,2150,1370,2032,2986,3207,2396,1238,2015,2958,2445,1602,2433,2565,1624,1210,2344,3191,2464,2873,2663,2332,2826,3314,2820,3297,3137,3065,3349,3556,3600,1687,1457,3144,1159,3535,1836,1787,1195,2211,1392,2228,3408,1740,1910,3595,2769,1402,2245,3467,2377,1953,2841,1111,1498,3102,3078,3237,1118,2498,1234,2157,2115,3482,3254,2100,1772,1259,2973,2359,1375,3218,1856,1540,3518,3386,2726,2631,2724,2858,2537,2268,3440,3060,3176,3018,1567,1329,3311,3143,1361,1182,1461,2868,1584,1937,2108,2551,2649,3294,3573,1419,2460,2798,1683,3000,2323,3179,2561,3210,1424,2312,1414,2053,3428,1810,1791,1214,3194,2349,1889,1644,1776,2598,1668,2243,2355,1984,3115,3333,1720,2756,2968,1114,2450,3486,1588,1297,2681,1530,2836,1382,2900,1831,3222,3540,2566,1799,1852,2813,2697,1246,2272,3364,3215,1525,2749,1991,2926,2203,1814,1779,2208,2883,2057,2963,1466,2440,1663,2221,2617,2423,2909,3476,1333,2546,3563,3279,3587,3183,3508,1895,1167,2189,2995,1510,2413,1680,3358,1219,1483,1273,1927,3289,2602,2894,1631,2121,2144,1146,1754,2292,1959,2556,3042,2585,2570,1747,2941,1595,3523,2524,3396,3387,3070,1916,1884,1615,1125,2657,1388,1795,2716,3404,2827,2959,3547,1833,2970,3319,2048,2938,1620,3472,1752,2393,3086,1652,1929,3283,2568,1535,2806,1226,2695,1256,3118,2029,3330,2935,3340,3123,2055,3579,1897,2425,1464,3302,1224,3170,3532,1139,1503,2193,3023,1707,3051,2891,1271,2442,2753,2148,2319,2510,2346,1574,2774,3419,3106,3197,2896,2065,2079,2361,2538,1408,1282,3251,2642,3155,2084,3238,2214,2383,2415,2493,2637,3551,1349,3270,2955,2299,1722,2669,1144,2802,3500,2871,1439,2197,1969,1307,2180,2824,2182,1877,2812,2742,3073,1993,2780,1731,1162,2757,3006,1149,2542,2252,2974,2605,2610,3055,1557,2314,2625,3165,1862,3034,2923,1325,1293,2278,2928,1177,2911,1820,1112,2578,1171,2075,2365,1474,2171,3110,2139,2288,2592,2207,2693,2867,1198,1841,1396,2401,1699,2051,2765,3423,1245,2481,2620,1445,1528,3159,2369,3241,1113,2797,3016,2633,2022,1477,3325,1726,2390,1250,1496,2303,2984,1973,1805,2506,3490,3380,1948,2952,1304,2784,2503,3146,2629,1340,1551,2582,1626,3009,3444,2239,3031,2816,2614,2096,1203,1208,3576,2665,3161,1905,3048,2684,3455,1472,3278,1958,2513,1547,3391,3376,2863,1961,2397,2661,3082,2012,1647,1252,3129,2720,2888,2831,2977,1611,1156,2060,1743,2678,2518,1368,2175,3058,2407,1267,1230,2850,3246,3448,2092,2224,3554,3202,1785,2337,3544,1658,2486,3412,1130,2468,1711,3080,2747,3305,2165,2688,3273,3063,2920,1188,2700,1186,3475,3026,2276,2219,1980,2128,1763,3127,3174,2044,1934,3356,2579,3388,3256,3366,2266,1240,2675,1404,1358,2247,2411,3488,1543,1766,3107,2838,2113,1141,2992,1802,3493,1702,2379,1221,1284,2975,1353,2357,1485,2711,1749,3224,1427,1797,3024,2860,2949,2722,2728,1717,1881,2807,2584,3398,2479,1966,3171,3533,3188,1517,2325,1781,1108,2865,1940,2435,2760,3400,2924,1839,3584,1918,3457,1316,1649,2352,3589,1459,2818,1180,1685,2885,2310,1844,1448,2187,3346,2110,1390,2305,2342,3056,2226,1453,1734,2792,1807,2907,1998,3593,2707,2594,2167,2283,2290,2135,2554,2532,3383,2004,1745,2026,1854,3252,2526,3085,3465,1276,1590,2098,3484,1674,2855,1639,3369,2823,2608,3235,3003,1822,3516,2130,2152,2262,1491,1689,3181,2399,3430,2330,2576,1193,2162,1212,2902,1442,2019,2421,2447,2944,3267,2462,2036,1309,1893,2294,2374,1578,2385,3291,2719,2233,3264,3100,3521,1986,3337,1757,1480,1908,2142,2930,2123,2258,1133,1642,2102,1512,1774,2534,2255,1593,3464,1380,3132,1248,2800,3328,2201,1816,3558,2746,1789,2961,2913,2795,3045,1346,2651,2549,1436,1859,1363,1314,2334,3560,1335,1693,2070,2572,1561,2704,3479,2417,2714,3196,3426,1891,2340,2668,1261,2430,2847,3360,1923,1597,1299,1120,2372,1236,2241,2159,3362,2731,2600,2898,3570,1384,1537,3538,1925,3076,3113,1902,3394,1505,1399,2270,3437,3432,1769,2453,1912,2177,1331,1606,2879,2640,3580,3461,2321,3227,2563,2881,1945,3212,3299,3096,1737,2887,1184,2690,2998,2438,2297,3316,2834,2993,3200,2191,1812,2106,2087,1468,2470,1417,1870,2771]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : SWV884-1 : TPTP v9.3.1. Released v4.1.0.
% 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
% 0.13/0.39  % Computer : n013.cluster.edu
% 0.13/0.39  % Model    : x86_64 x86_64
% 0.13/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39  % Memory   : 8046.5625MB
% 0.13/0.39  % OS       : Linux 6.8.0-71-generic
% 0.13/0.39  % CPULimit : 300
% 0.13/0.39  % WCLimit  : 300
% 0.13/0.39  % DateTime : Sat Sep 26 15:06:06 UTC 2026
% 0.13/0.39  % CPUTime  : 
% 0.13/0.39  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.88/0.97  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.45/1.40  % [INFO] 	 Parsing done (426ms). 
% 2.45/1.41  % [INFO] 	 Running in sequential loop mode. 
% 3.04/1.79  % [INFO] 	 eprover registered as external prover. 
% 3.04/1.80  % [INFO] 	 Scanning for conjecture ... 
% 4.03/2.03  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1114 axioms. Running axiom selection ... 
% 5.28/2.34  % [INFO] 	 Axiom selection finished. Selected 1100 axioms (removed 14 axioms). 
% 6.27/2.69  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 6.68/2.72  % [INFO] 	 Type checking passed. 
% 6.68/2.72  % [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 ... 
% 27.02/7.34  % External prover 'e' found a proof!
% 27.02/7.34  % [INFO] 	 Killing All external provers ... 
% 27.02/7.34  % Time passed: 6818ms (effective reasoning time: 5920ms)
% 27.02/7.35  % Axioms used in derivation (1100): cls_inj__image__mem__iff_1, cls_Suc__pred_0, cls_card__eq__SucD_2, cls_inf__sup__aci_I2_J_0, cls_less__iff__diff__less__0_0, cls_add__0__left_0, cls_add__pos__nonneg_0, cls_Int__absorb2_0, cls_Diff__iff_2, cls_eq__add__iff2_1, clsarity_nat__HOL_Oord, cls_vimage__code_0, cls_mult__eq__1__iff_1, clsarity_fun__Lattices_Olower__semilattice, cls_not__one__less__zero_0, cls_mult__less__cancel__left__disj_5, cls_finite__UNIV__card__ge__0_0, cls_Diff__cancel_0, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_one__le__mult__iff_1, cls_subset__insert_1, cls_dvd__mult__cancel1_0, cls_le__0__eq_1, cls_natgb_Oadd__r0__iff_1, cls_nat__dvd__not__less_0, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_order__le__less__trans_0, cls_mult__cancel2_0, cls_add__is__1_1, cls_less__diff__iff_1, cls_mult__zero__right_0, cls_zero__less__one_0, cls_nat__dvd__1__iff__1_1, cls_of__nat__add_0, cls_dvd_Oantisym__conv_0, cls_mult__nonneg__nonneg_0, cls_less__fun__def_1, cls_nat__mult__eq__1__iff_1, cls_Suc__inject_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_comm__semiring__class_Odistrib_0, cls_Suc__mono_0, cls_nat__0__less__mult__iff_1, cls_equalityI_0, cls_of__nat__0_0, cls_insert__inter__insert_0, cls_mod__mult__mult1_0, cls_add__less__cancel__left_1, cls_mult__right__mono_0, cls_insertE_0, cls_dvd__mult__right_0, cls_card__Diff__singleton_0, cls_dvd__mult2_0, cls_eq__imp__le_0, cls_le__diff__iff_0, cls_card__empty_0, cls_le__add__diff__inverse2_0, cls_Nat_Odiff__diff__eq_0, cls_le__diff__conv_1, cls_inj__on__iff__eq__card_0, cls_left__add__mult__distrib_0, cls_mult__less__cancel__right__disj_0, cls_subset__empty_1, cls_finite__insert_0, cls_sum__squares__eq__zero__iff_0, cls_one__is__add_4, cls_Suc__n__not__n_0, cls_nat__1__eq__mult__iff_0, cls_empty__is__image_1, cls_inj__image__eq__iff_0, cls_image__mono_0, cls_mult__is__0_2, cls_fun__upd__apply_1, cls_diff__Suc__1_0, cls_le__funD_0, cls_fun__upd__image_1, cls_xt1_I12_J_0, cls_subset__image__iff_2, cls_mult__nonneg__nonpos2_0, cls_card__Diff__insert_0, cls_inj__on__image__Int_0, cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_mult__less__cancel__left__disj_1, cls_zero__le__one_0, cls_insert__code_1, cls_nat__add__left__cancel__less_1, cls_termination__basic__simps_I5_J_0, cls_add__increasing2_0, cls_lift__Suc__mono__le_0, cls_Int__mono_0, cls_less__antisym_0, cls_le__iff__inf_1, cls_one__le__mult__iff_0, cls_less__add__Suc2_0, cls_of__nat__less__iff_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_eq__diff__iff_0, cls_card__insert_0, cls_card__Suc__eq_4, clsarity_bool__Lattices_Olower__semilattice, cls_mod__by__0_0, cls_add__is__1_2, cls_image__iff_0, cls_mod__mod__cancel_0, cls_finite__vimageI_0, cls_zero__le__mult__iff_3, cls_linorder__neqE_0, 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cls_mult__less__cancel__left__neg_1, cls_nat_Oinject_0, cls_add__lessD1_0, cls_inf__eq__top__eq2_0, cls_diff__less__mono_0, cls_even__less__0__iff_1, cls_less__SucE_0, cls_vimage__mono_0, cls_Int__left__absorb_0, cls_nat__1__eq__mult__iff_1, cls_card__inj__on__le_0, cls_sum__squares__gt__zero__iff_1, cls_Diff__disjoint_0, cls_order__neq__le__trans_0, cls_doubleton__eq__iff_3, cls_natgb_Onoteq__reduce_0, cls_psubset__insert__iff_0, cls_add__nonneg__nonneg_0, clsarity_nat__Ring__and__Field_Osemiring, cls_mult__mono_H_0, cls_less__diff__conv_1, cls_add__inf__distrib__right_0, cls_psubset__card__mono_0, cls_le__diff__conv_0, cls_mult__strict__left__mono__comm_0, cls_le__diff__conv2_0, cls_finite__Diff__insert_1, cls_inj__on__fun__updI_0, cls_Diff__Int__distrib_0, cls_finite__Diff2_1, cls_Diff__mono_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_psubset__subset__trans_0, cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0, cls_inj__on__def_0, 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cls_le__less__Suc__eq_0, cls_mult__less__cancel__left__pos_1, clsarity_bool__Lattices_Obounded__lattice, cls_finite__subset_0, cls_vimageE_0, cls_card__image_0, cls_natgb_Oadd__r0__iff_0, cls_less__eq__Suc__le_1, cls_le__eqI_0, cls_add__is__1_5, cls_nat__mult__less__cancel1_1, cls_mult__le__cancel__left__neg_0, cls_diff__self__eq__0_0, cls_less__Suc__eq__le_0, cls_insert__not__empty_0, cls_Int__left__commute_0, cls_mod__less__eq__dividend_0, cls_trans__less__add2_0, cls_zero__less__diff_0, cls_eq__card__imp__inj__on_0, cls_le0_0, cls_insert__subset_2, cls_full__nat__induct_1, cls_inf__bot__left_0, cls_inf1I_0, cls_card__Suc__eq_2, cls_zero__le__mult__iff_1, cls_add__is__1_4, cls_subsetD_0, cls_le__add2_0, cls_dvd__mult__cancel__left_1, cls_finite__imageD_0, cls_dvd__mult__cancel2_0, cls_card__bij__eq_0, cls_xt1_I11_J_0, cls_add__neg__neg_0, cls_inf__idem_0, cls_one__neq__zero_0, cls_double__eq__0__iff_0, clsarity_fun__Lattices_Obounded__lattice, cls_mult__le__0__iff_2, cls_add__eq__if_1, clsarity_fun__Complete__Lattice_Ocomplete__lattice, cls_mult__right__le__one__le_0, cls_mult__less__cancel2_0, cls_less__Suc0_0, cls_finite__Diff__insert_0, cls_mult__right__mono__neg_0, cls_sum__squares__eq__zero__iff_2, cls_le__add__right__mono_0, cls_subset__singletonD_0, cls_Int__iff_2, cls_vimage__code_1, cls_mult__1_0, cls_fun__upd__idem__iff_0, cls_card__Diff__singleton__if_1, cls_nat__add__left__cancel__le_0, cls_insert__absorb2_0, cls_class__semiring_Osemiring__rules_I18_J_0, cls_zmod__simps_I2_J_0, cls_dvd__mult__left_0, cls_mult__less__cancel1_2, cls_fun__upd__idem_0, cls_mod__mult__self2__is__0_0, cls_add__mult__distrib2_0, cls_inf__sup__aci_I4_J_0, cls_dvd_Ole__neq__trans_0, cls_mod__add__right__eq_0, cls_comm__monoid__add_Omult__left__commute_0, cls_vimage__singleton__eq_0, cls_diff__0__right_0, cls_xt1_I6_J_0, cls_subset__insert__iff_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_nat__le__add__iff2_1, cls_diff__Suc__less_0, cls_mult__less__cancel__left__disj_3, cls_zero__less__mult__pos2_0, cls_diff__le__self_0, cls_n__less__m__mult__n_0, cls_subset__image__iff_0, cls_doubleton__eq__iff_1, cls_nat__less__le_0, cls_mod__mult__eq_0, cls_mult__1__left_0, cls_nat_Osimps_I3_J_0, cls_subset__psubset__trans_0, cls_le__Suc__eq_2, cls_comm__monoid__add_Omult__1_0, cls_Diff__empty_0, cls_le__cube_0, cls_linorder__not__le_0, cls_nat__mult__eq__1__iff_0, cls_IntI_0, clsarity_nat__Ring__and__Field_Omult__mono1, cls_diff__add__assoc2_0, cls_mult__le__cancel2_0, cls_le__diff__conv2_1, cls_mod__mult__mult2_0, cls_mult__less__cancel__right__disj_4, cls_inf__greatest_0, cls_double__add__less__zero__iff__single__less__zero_1, cls_eq__add__iff2_0, cls_diff__less__mono2_0, cls_one__less__mult_0, cls_not__less__eq_0, cls_nat__le__linear_0, cls_trans__less__add1_0, cls_inv__into__injective_0, cls_less__trans__Suc_0, cls_plus__nat_Oadd__0_0, cls_dvd_Oeq__iff_2, cls_dvd__mult__cancel__right_0, clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_mult__zero__left_0, cls_nat__less__le_2, cls_mod__diff__left__eq_0, cls_dvd__mult__cancel1_1, cls_order__less__irrefl_0, cls_add__is__0_2, cls_eq__eqI_1, cls_less__diff__iff_0, cls_zero__less__diff_1, cls_minus__nat_Odiff__0_0, cls_less__fun__def_2, cls_add__is__1_3, cls_le__iff__inf_0, cls_dvd_Oless__trans_0, cls_le__iff__add_1, cls_subset__insert_0, cls_inc__induct_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_emptyE_0, cls_mod__mult__self3_0, clsarity_nat__Ring__and__Field_Opordered__semiring, cls_fun__upd__same_0, cls_dvd_Oorder__trans_0, cls_diff__is__0__eq_1, cls_diff__0__eq__0_0, cls_add__nonneg__eq__0__iff_2, cls_less__infI2_0, cls_Suc__n__not__le__n_0, cls_dvd__0__right_0, cls_comm__monoid__add_Ononempty__iff_2, cls_class__semiring_Oadd__c_0, cls_singleton__inject_0, cls_less__eqI_0, cls_nat__add__left__cancel_0, cls_subset__inj__on_0, cls_mult__pos__pos_0, cls_add__le__mono1_0, cls_dvd__diffD_0, cls_mult__left__le__imp__le_0, cls_dvd_Oneq__le__trans_0, cls_mult__strict__right__mono__neg_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_Suc__leD_0, cls_vimageI2_0, cls_add__eq__self__zero_0, clsarity_fun__Orderings_Opreorder, cls_le__diff__iff_1, cls_add__pos__pos_0, cls_split__mod_5, cls_add__mono_0, cls_mod__less__divisor_0, cls_Suc__eq__plus1_0, cls_sum__squares__gt__zero__iff_0, cls_nat__mult__dvd__cancel__disj_2, cls_dvd_Oantisym_0, cls_card__Suc__eq_5, cls_Int__greatest_0, cls_class__semiring_Osemiring__rules_I8_J_0, cls_n__not__Suc__n_0, cls_IntE_1, cls_mult__right__less__imp__less_0, cls_nat__less__add__iff1_1, cls_IntE_0, cls_image__subsetI_0, cls_nat__le__add__iff1_1, cls_inj__on__contraD_0, cls_inj__onD_0, cls_zmod__simps_I1_J_0, cls_less__SucI_0, cls_nat__mult__le__cancel1_0, cls_add__neg__nonpos_0, cls_Suc__le__D__lemma_1, cls_nat__0__less__mult__iff_2, cls_finite__surj__inj_0, cls_diffs0__imp__equal_0, cls_image__eqI_0, cls_subset__UNIV_0, cls_inf__le1_0, cls_insertCI_1, cls_inf__left__idem_0, cls_doubleton__eq__iff_4, cls_Max__in_0, cls_one__is__add_3, cls_card__insert__if_1, cls_not__less0_0, cls_le__infE_1, cls_card__Diff1__le_0, cls_mult__less__cancel__left__disj_2, cls_finite_OemptyI_0, cls_nat__mult__assoc_0, cls_card__eq__UNIV__imp__eq__UNIV_0, cls_Int__UNIV__left_0, cls_dvdI_0, cls_diff__add__inverse_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_inj__on__diff_0, cls_inj__on__insert_2, cls_inv__into__into_0, cls_nat__mult__commute_0, cls_dvd__diff__nat_0, cls_mult__less__cancel__right__disj_1, cls_eq__iff__diff__eq__0_1, cls_image__subset__iff_0, cls_finite__imageI_0, cls_add__less__cancel__left_0, cls_zmod__simps_I4_J_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_card__Diff2__less_0, cls_mult__eq__self__implies__10_0, cls_insert__code_0, cls_image__cong_0, cls_Diff__Int2_0, cls_order__less__imp__le_0, cls_add__leE_1, cls_Suc__pred_H_0, cls_mult__cancel1_0, cls_DiffE_1, cls_le__eqI_1, cls_Suc__diff__le_0, cls_Suc__less__eq_0, cls_subset__insertI_0, cls_mult__eq__0__iff_1, cls_le__iff__diff__le__0_1, cls_vimageD_0, cls_card__gt__0__iff_0, cls_add__gr__0_2, cls_diff__le__mono_0, cls_add__less__le__mono_0, cls_dvd__mod__imp__dvd_0, cls_inv__f__f_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_Diff__insert__absorb_0, cls_add__gr__0_1, cls_diff__commute_0, cls_insert__image_0, cls_rev__finite__subset_0, cls_image__vimage__eq_0, cls_le__less__Suc__eq_1, cls_less__Suc0_1, cls_nat__dvd__1__iff__1_0, cls_of__nat__Suc_0, clsarity_nat__Ring__and__Field_Omult__zero, cls_endo__inj__surj_0, cls_eq__iff__diff__eq__0_0, cls_insert__iff_2, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, cls_le__infI2_0, cls_dvd__mult_0, cls_fun__upd__upd_0, cls_mod__eq__0__iff_1, cls_le__add1_0, cls_psubset__insert__iff_2, cls_mod__if_0, cls_disjoint__iff__not__equal_0, cls_add__strict__increasing2_0, cls_le__add__diff_0, cls_termination__basic__simps_I2_J_0, cls_inf__top__left_0, cls_le__eq__less__or__eq_0, cls_vimage__empty_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_Suc__eq__plus1__left_0, cls_gfp__upperbound_0, cls_card__Diff__subset_0, cls_insert__commute_0, clsarity_nat__Orderings_Oorder, cls_xt1_I7_J_0, cls_nat__mult__less__cancel1_0, cls_image__is__empty_0, cls_dvd_Ole__less__trans_0, cls_psubset__insert__iff_7, cls_equalityE_0, cls_mult__le__less__imp__less_0, cls_natgb_Oadd__mul__solve_1, cls_imageI_0, cls_atLeast__subset__iff_0, cls_inf__bot__right_0, cls_zero__le__imp__of__nat_0, cls_finite__Diff2_0, cls_less__fun__def_0, cls_order__less__le_1, cls_mult__le__0__iff_3, cls_nat__mult__eq__cancel__disj_0, cls_mult__neg__neg_0, cls_linorder__not__less_1, cls_dvd__imp__le_0, cls_zero__less__Suc_0, cls_mult__less__cancel__left__neg_0, cls_class__semiring_Osemiring__rules_I4_J_0, cls_not__one__le__zero_0, cls_Min__in_0, cls_le__neq__implies__less_0, cls_le__add__iff2_0, cls_nat__less__le_1, cls_mult__less__le__imp__less_0, cls_add__le__cancel__left_0, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, cls_weak__coinduct__image_0, cls_dvd__diffD1_0, cls_mod__self_0, cls_less__eqI_1, cls_le__refl_0, clsarity_bool__Orderings_Otop, cls_not__less__eq__eq_0, cls_mod__Suc__eq__Suc__mod_0, cls_add__le__cancel__right_0, cls_mult__eq__1__iff_2, cls_mult__less__cancel__left__pos_0, cls_split__mult__neg__le_1, cls_nat__eq__add__iff2_1, cls_class__semiring_Osemiring__rules_I22_J_0, cls_add__diff__inverse_0, cls_mod__mult__distrib_0, cls_of__nat__less__0__iff_0, cls_image__inv__f__f_0, cls_subset__insert__iff_1, cls_dvd__mult__cancel__left_0, cls_even__less__0__iff_0, cls_le__SucI_0, cls_ball__empty_0, cls_finite__subset__image_0, cls_sum__squares__le__zero__iff_0, cls_inv__into__f__eq_0, cls_Int__insert__right_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_psubset__eq_2, cls_mult__cancel2_1, cls_mult__strict__left__mono__neg_0, cls_dvd__eq__mod__eq__0_1, cls_nat__add__commute_0, cls_Min__antimono_0, cls_Diff__subset_0, cls_predicate1D_0, cls_inf1E_0, cls_empty__Diff_0, cls_fun__upd__idem__iff_1, cls_zero__le__mult__iff_2, cls_dvd__0__left_0
% 27.02/7.35  % No. of inferences in proof: 2215
% 27.02/7.35  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6818 ms resp. 5920 ms w/o parsing
% 29.64/7.90  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 29.64/7.91  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------