TSTP Solution File: SWV693-1 by Leo-III---1.7.7

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.7
% Problem  : SWV693-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n021.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Fri May 19 12:17:54 EDT 2023

% Result   : Unsatisfiable 22.68s 6.51s
% Output   : Refutation 23.84s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      : 1539
% Syntax   : Number of formulae    : 2953 ( 453 unt; 126 typ;   0 def)
%            Number of atoms       : 8741 (1526 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives : 68824 (5432   ~;5914   |;   0   &;57478   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   33 (  12 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  190 ( 190   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :  128 ( 126 usr;   8 con; 0-5 aty)
%            Number of variables   : 8578 (   0   ^;8578   !;   0   ?;8578   :)

% Comments : 
%------------------------------------------------------------------------------
thf(hAPP_type,type,
    hAPP: $i > $i > $i ).

thf(c_Finite__Set_Osetsum_type,type,
    c_Finite__Set_Osetsum: $i > $i > $i ).

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

thf(tc_Complex_Ocomplex_type,type,
    tc_Complex_Ocomplex: $i ).

thf(c_COMBS_type,type,
    c_COMBS: $i > $i > $i > $i > $i > $i ).

thf(c_COMBB_type,type,
    c_COMBB: $i > $i > $i > $i ).

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

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

thf(c_COMBC_type,type,
    c_COMBC: $i > $i > $i > $i > $i ).

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

thf(c_Power_Opower__class_Opower_type,type,
    c_Power_Opower__class_Opower: $i > $i ).

thf(c_FFT__Mirabelle_Oroot_type,type,
    c_FFT__Mirabelle_Oroot: $i > $i ).

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

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

thf(v_i_type,type,
    v_i: $i ).

thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
    c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).

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

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

thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
    c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).

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

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

thf(c_SetInterval_Oord__class_OgreaterThanLessThan_type,type,
    c_SetInterval_Oord__class_OgreaterThanLessThan: $i > $i > $i > $i ).

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

thf(class_Int_Onumber_type,type,
    class_Int_Onumber: $i > $o ).

thf(c_Int_Onumber__class_Onumber__of_type,type,
    c_Int_Onumber__class_Onumber__of: $i > $i > $i ).

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

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

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

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

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

thf(c_HOL_Oord__class_Oless_type,type,
    c_HOL_Oord__class_Oless: $i > $i > $i ).

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

thf(class_Lattices_Oupper__semilattice_type,type,
    class_Lattices_Oupper__semilattice: $i > $o ).

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

thf(class_RealVector_Oreal__normed__vector_type,type,
    class_RealVector_Oreal__normed__vector: $i > $o ).

thf(c_Series_Osummable_type,type,
    c_Series_Osummable: $i > $i > $o ).

thf(c_Series_Osums_type,type,
    c_Series_Osums: $i > $i > $i > $o ).

thf(class_Ring__and__Field_Oordered__field_type,type,
    class_Ring__and__Field_Oordered__field: $i > $o ).

thf(class_Ring__and__Field_Odivision__by__zero_type,type,
    class_Ring__and__Field_Odivision__by__zero: $i > $o ).

thf(c_HOL_Oinverse__class_Odivide_type,type,
    c_HOL_Oinverse__class_Odivide: $i > $i ).

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

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

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

thf(class_Ring__and__Field_Odivision__ring_type,type,
    class_Ring__and__Field_Odivision__ring: $i > $o ).

thf(c_HOL_Oinverse__class_Oinverse_type,type,
    c_HOL_Oinverse__class_Oinverse: $i > $i ).

thf(class_Ring__and__Field_Ofield_type,type,
    class_Ring__and__Field_Ofield: $i > $o ).

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

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

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

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

thf(class_Int_Onumber__ring_type,type,
    class_Int_Onumber__ring: $i > $o ).

thf(c_Nat_Osemiring__1__class_Oof__nat_type,type,
    c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).

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

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

thf(class_RealVector_Ometric__space_type,type,
    class_RealVector_Ometric__space: $i > $o ).

thf(c_Lim_OisCont_type,type,
    c_Lim_OisCont: $i > $i > $i > $i > $o ).

thf(c_Lim_OLIM_type,type,
    c_Lim_OLIM: $i > $i > $i > $i > $i > $o ).

thf(class_RealVector_Oreal__normed__field_type,type,
    class_RealVector_Oreal__normed__field: $i > $o ).

thf(c_Deriv_Oderiv_type,type,
    c_Deriv_Oderiv: $i > $i > $i > $i > $o ).

thf(c_Series_Osuminf_type,type,
    c_Series_Osuminf: $i > $i > $i ).

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

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

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

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

thf(c_Deriv_Odifferentiable_type,type,
    c_Deriv_Odifferentiable: $i > $i > $i > $o ).

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

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

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

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

thf(class_Nat_Osemiring__char__0_type,type,
    class_Nat_Osemiring__char__0: $i > $o ).

thf(c_SetInterval_Oord__class_OatMost_type,type,
    c_SetInterval_Oord__class_OatMost: $i > $i > $i ).

thf(class_Int_Oring__char__0_type,type,
    class_Int_Oring__char__0: $i > $o ).

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

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

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

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

thf(c_SEQ_OLIMSEQ_type,type,
    c_SEQ_OLIMSEQ: $i > $i > $i > $o ).

thf(class_RealVector_Oreal__normed__algebra__1_type,type,
    class_RealVector_Oreal__normed__algebra__1: $i > $o ).

thf(c_SEQ_OCauchy_type,type,
    c_SEQ_OCauchy: $i > $i > $o ).

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

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

thf(class_RealVector_Oreal__normed__algebra_type,type,
    class_RealVector_Oreal__normed__algebra: $i > $o ).

thf(c_Limits_Otendsto_type,type,
    c_Limits_Otendsto: $i > $i > $i > $i > $i > $o ).

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

thf(class_Lattices_Obounded__lattice_type,type,
    class_Lattices_Obounded__lattice: $i > $o ).

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

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

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

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

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

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

thf(class_OrderedGroup_Oab__semigroup__idem__mult_type,type,
    class_OrderedGroup_Oab__semigroup__idem__mult: $i > $o ).

thf(class_Power_Opower_type,type,
    class_Power_Opower: $i > $o ).

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

thf(c_Complete__Lattice_OSup__class_OSup_type,type,
    c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).

thf(c_SEQ_OZseq_type,type,
    c_SEQ_OZseq: $i > $i > $o ).

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

thf(class_Ring__and__Field_Oring__1__no__zero__divisors_type,type,
    class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).

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

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

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

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

thf(c_FFT__Mirabelle_OIDFT_type,type,
    c_FFT__Mirabelle_OIDFT: $i > $i > $i > $i ).

thf(c_Limits_OZfun_type,type,
    c_Limits_OZfun: $i > $i > $i > $i > $o ).

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

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

thf(class_Lattices_Odistrib__lattice_type,type,
    class_Lattices_Odistrib__lattice: $i > $o ).

thf(c_SEQ_Osko__SEQ__XLIMSEQ__setsum__1__1_type,type,
    c_SEQ_Osko__SEQ__XLIMSEQ__setsum__1__1: $i > $i > $i > $i > $i > $i ).

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

thf(c_HOL_OIf_type,type,
    c_HOL_OIf: $i > $i ).

thf(class_RealVector_Oreal__normed__div__algebra_type,type,
    class_RealVector_Oreal__normed__div__algebra: $i > $o ).

thf(class_Ring__and__Field_Omult__mono_type,type,
    class_Ring__and__Field_Omult__mono: $i > $o ).

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

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

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

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

thf(c_FFT__Mirabelle_ODFT_type,type,
    c_FFT__Mirabelle_ODFT: $i > $i > $i > $i ).

thf(c_GCD_Ogcd__class_OLCM_type,type,
    c_GCD_Ogcd__class_OLCM: $i > $i > $i ).

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

thf(c_Finite__Set_Osetprod_type,type,
    c_Finite__Set_Osetprod: $i > $i > $i > $i > $i ).

thf(class_Ring__and__Field_Omult__mono1_type,type,
    class_Ring__and__Field_Omult__mono1: $i > $o ).

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

thf(class_RealVector_Oreal__field_type,type,
    class_RealVector_Oreal__field: $i > $o ).

thf(c_GCD_Ogcd__class_OGCD_type,type,
    c_GCD_Ogcd__class_OGCD: $i > $i > $i ).

thf(class_OrderedGroup_Olordered__ab__group__add__join_type,type,
    class_OrderedGroup_Olordered__ab__group__add__join: $i > $o ).

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

thf(338,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add__meet @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__left_0) ).

thf(2163,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add__meet @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(717,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).

thf(3021,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).

thf(631,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__add__zero_0) ).

thf(2822,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(1228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ C )
        = B )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).

thf(4201,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ C )
        = B )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1228]) ).

thf(308,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

thf(2094,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(1184,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ B @ A @ A ) @ E ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__divide__distrib_0) ).

thf(4094,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ B @ A @ A ) @ E ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1184]) ).

thf(218,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(1899,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(456,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).

thf(2427,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(1150,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ C @ E @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__diff_0) ).

thf(4015,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ C @ E @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1150]) ).

thf(1110,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add__join @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__left_0) ).

thf(3927,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add__join @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1110]) ).

thf(414,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).

thf(2331,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(784,axiom,
    class_Power_Opower @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).

thf(3172,plain,
    class_Power_Opower @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(121,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_1) ).

thf(1686,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(1388,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ A ) @ B ) @ C ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ F ) @ A )
      | ~ ( c_Deriv_Oderiv @ B @ ( hAPP @ C @ D ) @ E @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__chain_H_0) ).

thf(4560,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ A ) @ B ) @ C ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ F ) @ A )
      | ~ ( c_Deriv_Oderiv @ B @ ( hAPP @ C @ D ) @ E @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1388]) ).

thf(208,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).

thf(1879,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(135,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less1_0) ).

thf(1718,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(661,axiom,
    ! [A: $i] :
      ( A
     != ( hAPP @ c_Suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).

thf(2889,plain,
    ! [A: $i] :
      ( A
     != ( hAPP @ c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(183,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(1823,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(397,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).

thf(2295,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(402,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
       != ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).

thf(2306,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
       != ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(730,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__power_0) ).

thf(3053,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(861,axiom,
    class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

thf(3345,plain,
    class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(1145,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__square_0) ).

thf(4005,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1145]) ).

thf(1344,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).

thf(4464,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1344]) ).

thf(419,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).

thf(2341,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(712,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inverse_0) ).

thf(3008,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(315,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_8) ).

thf(2109,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Nat_Osemiring__char__0 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
       != ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).

thf(2031,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Nat_Osemiring__char__0 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
       != ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(998,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).

thf(3661,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[998]) ).

thf(157,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_2) ).

thf(1767,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(884,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).

thf(3399,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(263,axiom,
    ! [A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ A ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).

thf(1995,plain,
    ! [A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ A ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(1111,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__commute_0) ).

thf(3930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1111]) ).

thf(1214,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono_0) ).

thf(4169,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1214]) ).

thf(1055,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

thf(3798,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1055]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).

thf(1559,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(1000,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).

thf(3666,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).

thf(1153,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_2) ).

thf(4022,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1153]) ).

thf(450,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_4) ).

thf(2412,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(656,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( hAPP @ c_Suc @ B ) @ tc_nat )
        = ( c_Set_Oinsert @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ B @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThanSuc_0) ).

thf(2876,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( hAPP @ c_Suc @ B ) @ tc_nat )
        = ( c_Set_Oinsert @ B @ ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ B @ tc_nat ) @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(1220,axiom,
    ( ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_5) ).

thf(4183,plain,
    ( ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1220]) ).

thf(1266,axiom,
    class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

thf(4290,plain,
    class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1266]) ).

thf(917,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

thf(3477,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[917]) ).

thf(1014,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).

thf(3698,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(191,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).

thf(1840,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(964,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).

thf(3581,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(1082,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) )
        = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__cancel_0) ).

thf(3863,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) )
        = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1082]) ).

thf(1068,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__m__mult__n_0) ).

thf(3830,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1068]) ).

thf(195,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).

thf(1850,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(489,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

thf(2499,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(242,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_0) ).

thf(1950,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(62,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).

thf(1549,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(149,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_1) ).

thf(1750,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(683,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ E ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__left__distrib_0) ).

thf(2940,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ E ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(1177,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).

thf(4075,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1177]) ).

thf(529,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).

thf(2590,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

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

thf(3098,plain,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(563,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).

thf(2671,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(139,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ B )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_1) ).

thf(1728,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ B )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(310,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).

thf(2099,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(1284,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C ) ) @ D ) @ tc_nat ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ D ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_0) ).

thf(4326,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C ) ) @ D ) @ tc_nat ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ D ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1284]) ).

thf(1351,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel2_0) ).

thf(4479,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1351]) ).

thf(429,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono_0) ).

thf(2363,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(1161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_0) ).

thf(4043,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1161]) ).

thf(1007,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_1) ).

thf(3681,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).

thf(1138,axiom,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).

thf(3990,plain,
    ! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1138]) ).

thf(1159,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).

thf(4037,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1159]) ).

thf(403,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).

thf(2309,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(739,axiom,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

thf(3072,plain,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(359,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).

thf(2210,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(850,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono2_0) ).

thf(3317,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(1360,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

thf(4500,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1360]) ).

thf(368,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).

thf(2231,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(542,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

thf(2622,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(1277,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ C ) ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ C ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_0) ).

thf(4311,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ C ) ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ C ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1277]) ).

thf(625,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) @ B ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split__asm_1) ).

thf(2808,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) @ B ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).

thf(1100,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).

thf(3905,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Oorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1100]) ).

thf(50,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).

thf(1522,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(811,axiom,
    class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).

thf(3230,plain,
    class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[811]) ).

thf(437,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).

thf(2381,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(1062,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ c_Suc @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__shift_0) ).

thf(3813,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ c_Suc @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1062]) ).

thf(487,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OisCont @ C @ D @ A @ B )
      | ~ ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ A ) @ C ) @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ C @ D ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__iff_1) ).

thf(2495,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OisCont @ C @ D @ A @ B )
      | ~ ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ A ) @ C ) @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ C @ D ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(669,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).

thf(2908,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(293,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc2_0) ).

thf(2062,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(949,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__mult2_0) ).

thf(3549,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[949]) ).

thf(610,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).

thf(2776,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(176,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(1808,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(559,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ D @ B @ A @ A ) ) @ E )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__subtractf_0) ).

thf(2659,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ D @ B @ A @ A ) ) @ E )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(892,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).

thf(3417,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[892]) ).

thf(931,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_Finite__Set_Osetprod @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ C @ E @ B @ A ) ) @ ( c_Finite__Set_Osetprod @ D @ E @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__timesf_0) ).

thf(3509,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_Finite__Set_Osetprod @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Finite__Set_Osetprod @ C @ E @ B @ A ) ) @ ( c_Finite__Set_Osetprod @ D @ E @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(834,axiom,
    class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__0) ).

thf(3285,plain,
    class_Ring__and__Field_Ocomm__semiring__0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(910,axiom,
    ! [A: $i] :
      ( ( c_GCD_Ogcd__class_OLCM @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_nat ) @ tc_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_OSup__singleton_0) ).

thf(3460,plain,
    ! [A: $i] :
      ( ( c_GCD_Ogcd__class_OLCM @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_nat ) @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[910]) ).

thf(4,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__exp_0) ).

thf(1422,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(686,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Limits_OZfun @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ D @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__Zfun__iff_0) ).

thf(2947,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Limits_OZfun @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ D @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(55,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).

thf(1533,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(1412,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) @ A ) ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_1) ).

thf(4614,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) @ A ) ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1412]) ).

thf(885,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__cube_0) ).

thf(3402,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[885]) ).

thf(11,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).

thf(1437,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(1404,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).

thf(4592,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1404]) ).

thf(352,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_8) ).

thf(2195,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(114,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).

thf(1671,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(901,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).

thf(3439,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(595,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complete__lattice__class_OSup__singleton_0) ).

thf(2740,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(142,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

thf(1735,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(821,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).

thf(3253,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ B )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[821]) ).

thf(642,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_Series_Osuminf @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) @ ( c_Series_Osuminf @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) @ A ) ) )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_suminf__split__initial__segment_0) ).

thf(2844,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_Series_Osuminf @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) @ ( c_Series_Osuminf @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) @ A ) ) )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).

thf(20,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).

thf(1458,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(167,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).

thf(1788,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osummable @ B @ A )
      | ~ ( c_Series_Osums @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__summable_0) ).

thf(1426,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osummable @ B @ A )
      | ~ ( c_Series_Osums @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(536,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).

thf(2607,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(571,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I27_J_0) ).

thf(2686,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(1117,axiom,
    class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).

thf(3942,plain,
    class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1117]) ).

thf(993,axiom,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

thf(3649,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[993]) ).

thf(769,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse_0) ).

thf(3135,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[769]) ).

thf(1185,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less_0) ).

thf(4097,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1185]) ).

thf(1191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq__number__of_1) ).

thf(4110,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1191]) ).

thf(203,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( c_HOL_Oone__class_Oone @ A ) )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).

thf(1867,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( c_HOL_Oone__class_Oone @ A ) )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(265,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_2) ).

thf(1999,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(904,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__diff__less_0) ).

thf(3446,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[904]) ).

thf(467,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(2448,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(680,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).

thf(2933,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(460,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).

thf(2434,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(582,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ ( hAPP @ c_Suc @ B ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__Suc_0) ).

thf(2712,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ ( hAPP @ c_Suc @ B ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(979,axiom,
    class_Ring__and__Field_Osemiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

thf(3616,plain,
    class_Ring__and__Field_Osemiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(1260,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_OZfun @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ C @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OZfun_0) ).

thf(4279,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_OZfun @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ C @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1260]) ).

thf(1048,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).

thf(3781,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1048]) ).

thf(1335,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).

thf(4440,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1335]) ).

thf(1012,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__less__n__mult__m_0) ).

thf(3693,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).

thf(1390,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).

thf(4564,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1390]) ).

thf(479,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).

thf(2476,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(544,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_0) ).

thf(2627,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(340,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_7) ).

thf(2168,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(1168,axiom,
    class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).

thf(4058,plain,
    class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1168]) ).

thf(891,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).

thf(3414,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(154,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).

thf(1761,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(762,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).

thf(3121,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(956,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).

thf(3562,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[956]) ).

thf(100,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).

thf(1640,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(524,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_7) ).

thf(2580,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(666,axiom,
    class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).

thf(2901,plain,
    class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(848,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono2_0) ).

thf(3313,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(1332,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Osummable_0) ).

thf(4435,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1332]) ).

thf(284,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).

thf(2042,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(1022,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_OZfun @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) ) @ D ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ D @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__mult__right_0) ).

thf(3717,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_OZfun @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) ) @ D ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ D @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1022]) ).

thf(428,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).

thf(2360,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(873,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).

thf(3370,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(1163,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_Otendsto @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ D ) @ F @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ E @ F @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Otendsto_0) ).

thf(4047,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_Otendsto @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ D ) @ F @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ E @ F @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1163]) ).

thf(189,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ C @ D @ ( hAPP @ C @ D ) @ A @ B )
      | ~ ( c_Lim_OisCont @ C @ D @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__def_0) ).

thf(1835,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ C @ D @ ( hAPP @ C @ D ) @ A @ B )
      | ~ ( c_Lim_OisCont @ C @ D @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(1292,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).

thf(4343,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1292]) ).

thf(286,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_6) ).

thf(2046,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(1141,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

thf(3994,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1141]) ).

thf(164,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).

thf(1782,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(928,axiom,
    class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).

thf(3502,plain,
    class_Int_Oring__char__0 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[928]) ).

thf(933,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Limits_OZfun @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ D @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ C @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__add_0) ).

thf(3513,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Limits_OZfun @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ D @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ C @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(747,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).

thf(3088,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Obot @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).

thf(1197,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).

thf(4124,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1197]) ).

thf(660,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ ( hAPP @ c_Suc @ D ) @ tc_nat ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__op__ivl__Suc_0) ).

thf(2886,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ ( hAPP @ c_Suc @ D ) @ tc_nat ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(83,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).

thf(1601,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(495,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_2) ).

thf(2516,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(296,axiom,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).

thf(2067,plain,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(1282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( hAPP @ c_Suc @ C ) @ ( hAPP @ c_Suc @ D ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ c_Suc ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__shift__bounds__Suc__ivl_0) ).

thf(4322,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( hAPP @ c_Suc @ C ) @ ( hAPP @ c_Suc @ D ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ c_Suc ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1282]) ).

thf(501,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).

thf(2531,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(147,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osums @ B @ ( c_Series_Osuminf @ B @ A ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__sums_0) ).

thf(1746,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osums @ B @ ( c_Series_Osuminf @ B @ A ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(754,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__cancel_0) ).

thf(3103,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(947,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ A @ A @ A ) @ C ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ E ) @ C ) @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__cdivide_0) ).

thf(3545,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ A @ A @ A ) @ C ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ E ) @ C ) @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[947]) ).

thf(587,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__vector @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ A @ B ) @ C ) @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ B ) @ D ) ) @ ( c_HOL_Ozero__class_Ozero @ B ) @ E @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ D @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__offset__zero_0) ).

thf(2723,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__vector @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ A @ B ) @ C ) @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ B ) @ D ) ) @ ( c_HOL_Ozero__class_Ozero @ B ) @ E @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ D @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(1304,axiom,
    class_Ring__and__Field_Omult__zero @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

thf(4371,plain,
    class_Ring__and__Field_Omult__zero @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1304]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
       != ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).

thf(1441,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
       != ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(1255,axiom,
    ! [A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).

thf(4266,plain,
    ! [A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1255]) ).

thf(104,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).

thf(1650,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(102,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

thf(1645,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(1227,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc_0) ).

thf(4198,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1227]) ).

thf(1097,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).

thf(3898,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1097]) ).

thf(771,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_0) ).

thf(3140,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(28,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).

thf(1475,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(48,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__add_1) ).

thf(1518,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(129,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).

thf(1703,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(1010,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatMost @ ( hAPP @ c_Suc @ C ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatMost @ C @ tc_nat ) ) ) @ ( hAPP @ B @ ( hAPP @ c_Suc @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__atMost__Suc_0) ).

thf(3688,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatMost @ ( hAPP @ c_Suc @ C ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatMost @ C @ tc_nat ) ) ) @ ( hAPP @ B @ ( hAPP @ c_Suc @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1010]) ).

thf(653,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_2) ).

thf(2869,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(1366,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( hAPP @ c_Suc @ B ) @ tc_nat )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThanSuc_1) ).

thf(4511,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( hAPP @ c_Suc @ B ) @ tc_nat )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1366]) ).

thf(1248,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).

thf(4249,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1248]) ).

thf(212,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).

thf(1887,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(1310,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) @ A ) ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_1) ).

thf(4386,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) @ A ) ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1310]) ).

thf(690,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).

thf(2957,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).

thf(1094,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Osummable_0) ).

thf(3891,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1094]) ).

thf(1334,axiom,
    class_Lattices_Olower__semilattice @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).

thf(4439,plain,
    class_Lattices_Olower__semilattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1334]) ).

thf(830,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

thf(3275,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(418,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).

thf(2339,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(1323,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

thf(4415,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1323]) ).

thf(1238,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

thf(4224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1238]) ).

thf(1065,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_1) ).

thf(3821,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1065]) ).

thf(222,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).

thf(1907,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(995,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__right__cancel_0) ).

thf(3653,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(388,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_7) ).

thf(2274,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(1046,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__pwr_0) ).

thf(3776,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1046]) ).

thf(764,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(3125,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(516,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(2562,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(578,axiom,
    class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0) ).

thf(2703,plain,
    class_Ring__and__Field_Osemiring__0 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).

thf(1378,axiom,
    class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).

thf(4539,plain,
    class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1378]) ).

thf(1244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_0) ).

thf(4238,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1244]) ).

thf(800,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).

thf(3204,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[800]) ).

thf(1115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).

thf(3938,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1115]) ).

thf(720,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osums @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__mult2_0) ).

thf(3029,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osums @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).

thf(1294,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).

thf(4348,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1294]) ).

thf(895,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ D ) ) )
      | ( C = D )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__scale__eq__noteq_0) ).

thf(3425,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ D ) ) )
      | ( C = D )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[895]) ).

thf(169,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_5) ).

thf(1792,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_9) ).

thf(1430,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(593,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).

thf(2735,plain,
    ! [B: $i,A: $i] :
      ( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
      | ~ ( class_Orderings_Opreorder @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(258,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).

thf(1985,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(1326,axiom,
    class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).

thf(4422,plain,
    class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1326]) ).

thf(767,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).

thf(3131,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(109,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(1660,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(1174,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) ) @ D ) @ E @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ F ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ F @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OLIM_0) ).

thf(4070,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) ) @ D ) @ E @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ F ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ F @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1174]) ).

thf(759,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).

thf(3116,plain,
    class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[759]) ).

thf(980,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

thf(3617,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).

thf(465,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ A ) @ C ) @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ C @ D ) @ A @ B )
      | ~ ( c_Lim_OisCont @ C @ D @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__iff_0) ).

thf(2444,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ A ) @ C ) @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ C @ D ) @ A @ B )
      | ~ ( c_Lim_OisCont @ C @ D @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(200,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_2) ).

thf(1860,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(1288,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_OZfun @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ C @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__mult__left_0) ).

thf(4334,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_OZfun @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ C @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1288]) ).

thf(362,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_2) ).

thf(2217,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(1200,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ ( hAPP @ c_Suc @ D ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) ) ) @ ( hAPP @ B @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__op__ivl__Suc_1) ).

thf(4130,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ ( hAPP @ c_Suc @ D ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) ) ) @ ( hAPP @ B @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1200]) ).

thf(945,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).

thf(3542,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(889,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ F ) @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__diff_0) ).

thf(3410,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ F ) @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[889]) ).

thf(348,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).

thf(2185,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(832,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).

thf(3280,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
       != ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[832]) ).

thf(1057,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__shift__lb__Suc0__0__upt_0) ).

thf(3803,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1057]) ).

thf(474,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

thf(2466,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(1329,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) @ D @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__linear_0) ).

thf(4428,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) @ D @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1329]) ).

thf(726,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).

thf(3043,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).

thf(1078,axiom,
    class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).

thf(3855,plain,
    class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1078]) ).

thf(597,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_1) ).

thf(2745,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(426,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).

thf(2356,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(520,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).

thf(2571,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(1020,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).

thf(3713,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(1195,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Suc @ A )
       != ( hAPP @ c_Suc @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).

thf(4119,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Suc @ A )
       != ( hAPP @ c_Suc @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1195]) ).

thf(879,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).

thf(3385,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[879]) ).

thf(1296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).

thf(4353,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1296]) ).

thf(71,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

thf(1572,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(805,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) )
      | ( B
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_geometric__sum_0) ).

thf(3216,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) )
      | ( B
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).

thf(1741,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(1384,axiom,
    class_Orderings_Oorder @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).

thf(4551,plain,
    class_Orderings_Oorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1384]) ).

thf(1121,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Opower @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) ) @ tc_nat @ A @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ c_Suc @ D ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ tc_nat @ A @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ c_Suc @ D ) @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__realpow__rev__sumr_0) ).

thf(3951,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Opower @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) ) @ tc_nat @ A @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ c_Suc @ D ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ tc_nat @ A @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ c_Suc @ D ) @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1121]) ).

thf(160,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

thf(1773,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(248,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I4_J_0) ).

thf(1963,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(827,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( c_SEQ_OLIMSEQ @ B @ C @ A )
      | ~ ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ D ) ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__offset_0) ).

thf(3268,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( c_SEQ_OLIMSEQ @ B @ C @ A )
      | ~ ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ D ) ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(194,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).

thf(1847,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(60,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).

thf(1545,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(453,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__algebra__1 @ B )
      | ( C = D )
      | ~ ( c_Lim_OLIM @ E @ F @ D @ B @ A )
      | ~ ( c_Lim_OLIM @ E @ F @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__unique_0) ).

thf(2420,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__algebra__1 @ B )
      | ( C = D )
      | ~ ( c_Lim_OLIM @ E @ F @ D @ B @ A )
      | ~ ( c_Lim_OLIM @ E @ F @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(229,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).

thf(1922,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(573,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).

thf(2691,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(752,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

thf(3099,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).

thf(172,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_7) ).

thf(1800,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(1225,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

thf(4194,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1225]) ).

thf(1298,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_0) ).

thf(4358,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1298]) ).

thf(511,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).

thf(2552,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(30,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_8) ).

thf(1479,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(87,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

thf(1609,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(548,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).

thf(2635,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(678,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono2_0) ).

thf(2929,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(714,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ D ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ ( hAPP @ c_Suc @ D ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__imp__le__base_0) ).

thf(3014,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ D ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ ( hAPP @ c_Suc @ D ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(1204,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

thf(4141,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1204]) ).

thf(1309,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D )
        = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).

thf(4383,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D )
        = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1309]) ).

thf(400,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

thf(2301,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(179,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Lim_OisCont @ B @ C @ A @ A )
      | ~ ( c_Deriv_Oderiv @ B @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__isCont_0) ).

thf(1815,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Lim_OisCont @ B @ C @ A @ A )
      | ~ ( c_Deriv_Oderiv @ B @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(1342,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Lim_OisCont @ ( hAPP @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ A ) @ A @ A @ A ) @ B ) @ C @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OisCont_0) ).

thf(4460,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Lim_OisCont @ ( hAPP @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ A ) @ A @ A @ A ) @ B ) @ C @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1342]) ).

thf(37,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).

thf(1494,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(1312,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__add__const_0) ).

thf(4390,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1312]) ).

thf(1347,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ B @ C @ A )
      | ~ ( c_SEQ_OLIMSEQ @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ D ) @ B @ tc_nat @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__diff__approach__zero2_0) ).

thf(4471,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ B @ C @ A )
      | ~ ( c_SEQ_OLIMSEQ @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ D ) @ B @ tc_nat @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1347]) ).

thf(953,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing_0) ).

thf(3557,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).

thf(206,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).

thf(1875,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(645,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(2852,plain,
    class_Orderings_Oorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(812,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A )
      | ~ ( c_Series_Osummable @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__mult_0) ).

thf(3231,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A )
      | ~ ( c_Series_Osummable @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(1083,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).

thf(3866,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1083]) ).

thf(502,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
        = B )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_0) ).

thf(2533,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
        = B )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(1273,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBS__def_0) ).

thf(4302,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1273]) ).

thf(1367,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__0_0) ).

thf(4514,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1367]) ).

thf(634,axiom,
    hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ v_i @ tc_nat ) @ v_n ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(2829,plain,
    hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ v_i @ tc_nat ) @ v_n ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(1051,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B )
      = ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc_0) ).

thf(3788,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B )
      = ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1051]) ).

thf(1405,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( B
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

thf(4595,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( B
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1405]) ).

thf(371,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).

thf(2237,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(852,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).

thf(3322,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(897,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(3431,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(111,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).

thf(1664,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(382,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).

thf(2259,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(555,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).

thf(2650,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).

thf(299,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(2073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(272,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).

thf(2017,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(345,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

thf(2178,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(364,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(2222,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(540,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) @ A ) ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq2_0) ).

thf(2616,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) @ A ) ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(1315,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_0) ).

thf(4396,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1315]) ).

thf(1092,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono1_0) ).

thf(3887,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1092]) ).

thf(277,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__add__less2_0) ).

thf(2027,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(1216,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OZseq @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A )
      | ~ ( c_SEQ_OZseq @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OZseq_0) ).

thf(4173,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OZseq @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A )
      | ~ ( c_SEQ_OZseq @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1216]) ).

thf(1113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OZseq @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A )
      | ~ ( c_SEQ_OZseq @ C @ A )
      | ~ ( c_SEQ_OZseq @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__diff_0) ).

thf(3934,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OZseq @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A )
      | ~ ( c_SEQ_OZseq @ C @ A )
      | ~ ( c_SEQ_OZseq @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1113]) ).

thf(1336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__mult_0) ).

thf(4443,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1336]) ).

thf(1175,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).

thf(4072,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1175]) ).

thf(177,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__lessD1_0) ).

thf(1811,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(1396,axiom,
    class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__field) ).

thf(4578,plain,
    class_RealVector_Oreal__field @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1396]) ).

thf(313,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

thf(2105,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(306,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_1) ).

thf(2090,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(882,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__num_0) ).

thf(3393,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(1252,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).

thf(4258,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1252]) ).

thf(1025,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).

thf(3724,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1025]) ).

thf(224,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).

thf(1911,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(1340,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) )
      | ( B = C )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel__disj_0) ).

thf(4454,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) )
      | ( B = C )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1340]) ).

thf(839,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) @ D ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) @ B ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__add__mult__distrib_0) ).

thf(3295,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) @ D ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) @ B ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(907,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).

thf(3453,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(468,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_Int_Onumber @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).

thf(2451,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_Int_Onumber @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(199,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_5) ).

thf(1858,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(1206,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).

thf(4147,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ B @ C )
     != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1206]) ).

thf(938,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff__rev__if_1) ).

thf(3525,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(185,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add2_0) ).

thf(1828,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(676,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).

thf(2925,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).

thf(1677,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(280,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_8) ).

thf(2034,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(1108,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ C @ E @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__add_0) ).

thf(3923,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ C @ E @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1108]) ).

thf(837,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( B
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_1) ).

thf(3290,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( B
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(841,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

thf(3300,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[841]) ).

thf(749,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).

thf(3093,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(1193,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).

thf(4115,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1193]) ).

thf(416,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add1_0) ).

thf(2335,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(611,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OZseq @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A )
      | ~ ( c_SEQ_OZseq @ C @ A )
      | ~ ( c_SEQ_OZseq @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__mult_0) ).

thf(2777,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OZseq @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A )
      | ~ ( c_SEQ_OZseq @ C @ A )
      | ~ ( c_SEQ_OZseq @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(776,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Odiff__diff__eq_0) ).

thf(3152,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(291,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__le__add2_0) ).

thf(2058,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(431,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).

thf(2367,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(1241,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ F ) @ D ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OLIM_0) ).

thf(4230,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ F ) @ D ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1241]) ).

thf(649,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).

thf(2861,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(482,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osummable @ B @ A )
      | ~ ( c_Series_Osums @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__iff_0) ).

thf(2483,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osummable @ B @ A )
      | ~ ( c_Series_Osums @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(92,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

thf(1622,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(550,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).

thf(2639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(854,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

thf(3327,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(312,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).

thf(2103,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(809,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_2) ).

thf(3226,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(1369,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I3_J_0) ).

thf(4519,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1369]) ).

thf(1085,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_0) ).

thf(3870,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1085]) ).

thf(585,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( hAPP @ c_Suc @ B ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc__right_0) ).

thf(2718,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( hAPP @ c_Suc @ B ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(793,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).

thf(3189,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(391,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add1_0) ).

thf(2281,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(1059,axiom,
    ! [A: $i] :
      ( ( c_GCD_Ogcd__class_OGCD @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_nat ) @ tc_nat )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gcd__lcm__complete__lattice__nat_OInf__singleton_0) ).

thf(3808,plain,
    ! [A: $i] :
      ( ( c_GCD_Ogcd__class_OGCD @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_nat ) @ tc_nat )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1059]) ).

thf(498,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

thf(2523,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(52,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).

thf(1526,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(327,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide__number__of_0) ).

thf(2137,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(1160,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Odiff_0) ).

thf(4040,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1160]) ).

thf(869,axiom,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_4) ).

thf(3361,plain,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[869]) ).

thf(1037,axiom,
    class_Lattices_Oupper__semilattice @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).

thf(3756,plain,
    class_Lattices_Oupper__semilattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1037]) ).

thf(1376,axiom,
    class_Int_Onumber @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).

thf(4536,plain,
    class_Int_Onumber @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1376]) ).

thf(127,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

thf(1697,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(954,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) @ D ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ D ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff2_0) ).

thf(3559,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) @ D ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ D ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[954]) ).

thf(1264,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ c_Suc @ B ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__Suc_0) ).

thf(4285,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( hAPP @ c_Suc @ B ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1264]) ).

thf(974,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ tc_nat @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ A ) ) @ B ) @ A @ tc_nat @ A ) @ C ) @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__power_0) ).

thf(3606,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ tc_nat @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ A ) ) @ B ) @ A @ tc_nat @ A ) @ C ) @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[974]) ).

thf(1402,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).

thf(4588,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1402]) ).

thf(791,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_0) ).

thf(3184,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(527,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_4) ).

thf(2586,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(701,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__Suc_0) ).

thf(2982,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).

thf(659,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) ) @ D ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__mult__right__zero_0) ).

thf(2884,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) ) @ D ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(253,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_1) ).

thf(1975,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(68,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).

thf(1564,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(605,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ A ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ C @ A ) ) @ D ) @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ E ) ) @ F )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) @ ( c_Finite__Set_Osetsum @ B @ A ) ) @ ( c_COMBC @ D @ B @ C @ A ) ) @ C @ ( tc_fun @ B @ tc_bool ) @ A ) @ F ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__commute_0) ).

thf(2762,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ C @ A ) @ ( tc_fun @ ( tc_fun @ C @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ C @ A ) ) @ D ) @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ E ) ) @ F )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ C ) @ ( c_Finite__Set_Osetsum @ B @ A ) ) @ ( c_COMBC @ D @ B @ C @ A ) ) @ C @ ( tc_fun @ B @ tc_bool ) @ A ) @ F ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(876,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) @ A ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).

thf(3378,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) @ A ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(899,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).

thf(3435,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(689,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_0) ).

thf(2954,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).

thf(1319,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ C )
        = ( c_Series_Osuminf @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A ) )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Osuminf_0) ).

thf(4407,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ C )
        = ( c_Series_Osuminf @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A ) )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1319]) ).

thf(124,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

thf(1691,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(521,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

thf(2574,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(594,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc_0) ).

thf(2737,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(551,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).

thf(2641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(1054,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).

thf(3795,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1054]) ).

thf(723,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).

thf(3037,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).

thf(713,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).

thf(3011,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).

thf(1408,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib_0) ).

thf(4604,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1408]) ).

thf(906,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).

thf(3450,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(929,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).

thf(3503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[929]) ).

thf(1234,axiom,
    class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).

thf(4216,plain,
    class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1234]) ).

thf(968,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).

thf(3591,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[968]) ).

thf(842,axiom,
    hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).

thf(3301,plain,
    hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(356,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_3) ).

thf(2204,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(1136,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
      | ( c_Limits_Otendsto @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( c_HOL_Oinverse__class_Oinverse @ A ) ) @ C ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ D ) @ E @ B @ A )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Limits_Otendsto @ C @ D @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__inverse_0) ).

thf(3984,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
      | ( c_Limits_Otendsto @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( c_HOL_Oinverse__class_Oinverse @ A ) ) @ C ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ D ) @ E @ B @ A )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Limits_Otendsto @ C @ D @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1136]) ).

thf(783,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
      | ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).

thf(3169,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[783]) ).

thf(826,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).

thf(3265,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[826]) ).

thf(1077,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

thf(3852,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1077]) ).

thf(1374,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__assoc_0) ).

thf(4531,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1374]) ).

thf(26,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono_0) ).

thf(1470,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(226,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
       != B )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).

thf(1915,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
       != B )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(131,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

thf(1708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(1042,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_1) ).

thf(3767,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1042]) ).

thf(1395,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__left_0) ).

thf(4576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1395]) ).

thf(303,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).

thf(2083,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(1157,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).

thf(4031,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1157]) ).

thf(1169,axiom,
    ( ( c_GCD_Ogcd__class_OGCD @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_nat )
    = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_GCD__empty__nat_0) ).

thf(4059,plain,
    ( ( c_GCD_Ogcd__class_OGCD @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_nat )
    = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1169]) ).

thf(668,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__add_0) ).

thf(2905,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(609,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left__number__of_0) ).

thf(2773,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).

thf(98,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).

thf(1636,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(564,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).

thf(2673,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(1029,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_2) ).

thf(3735,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1029]) ).

thf(384,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).

thf(2264,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_Series_Osuminf @ B @ A )
        = C )
      | ~ ( c_Series_Osums @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__iff_1) ).

thf(1723,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_Series_Osuminf @ B @ A )
        = C )
      | ~ ( c_Series_Osums @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(824,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_0) ).

thf(3261,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(1345,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ E @ tc_nat ) ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ D @ tc_nat ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ tc_nat ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff__nat__ivl_0) ).

thf(4466,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ E @ tc_nat ) ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ D @ tc_nat ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ tc_nat ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1345]) ).

thf(506,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(2541,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(74,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(1580,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(1306,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).

thf(4375,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1306]) ).

thf(331,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).

thf(2147,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(976,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_SEQ_OLIMSEQ @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) @ A )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_SEQ_OLIMSEQ @ C @ E @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__divide_0) ).

thf(3610,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_SEQ_OLIMSEQ @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) @ A )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_SEQ_OLIMSEQ @ C @ E @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[976]) ).

thf(737,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).

thf(3069,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(1263,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).

thf(4284,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1263]) ).

thf(703,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( c_SEQ_OLIMSEQ @ B @ C @ A )
      | ~ ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ c_Suc ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__Suc__iff_0) ).

thf(2986,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( c_SEQ_OLIMSEQ @ B @ C @ A )
      | ~ ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ c_Suc ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(999,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).

thf(3664,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(534,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).

thf(2601,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
       != ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(1067,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

thf(3827,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1067]) ).

thf(515,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_6) ).

thf(2560,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(1130,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_3) ).

thf(3972,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1130]) ).

thf(377,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_1) ).

thf(2249,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(973,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_0) ).

thf(3603,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__eq__less_0) ).

thf(1519,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(532,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_4) ).

thf(2596,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(1410,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).

thf(4609,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
      | ( A
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1410]) ).

thf(70,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(1570,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_1) ).

thf(1502,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(1249,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__assoc_0) ).

thf(4252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1249]) ).

thf(813,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ C @ D @ E @ B @ A )
      | ~ ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ B @ A @ A ) @ E ) @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__zero__iff_0) ).

thf(3233,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ C @ D @ E @ B @ A )
      | ~ ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ B @ A @ A ) @ E ) @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(1229,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Limits_OZfun @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ C @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_OZfun_0) ).

thf(4204,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Limits_OZfun @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ C @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1229]) ).

thf(1091,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A ) ) @ C ) ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_1) ).

thf(3884,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A ) ) @ C ) ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1091]) ).

thf(1338,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_1) ).

thf(4449,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1338]) ).

thf(1357,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv2_0) ).

thf(4493,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1357]) ).

thf(325,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Int_Oring__char__0 @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).

thf(2132,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Int_Oring__char__0 @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(820,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(3250,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(801,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).

thf(3207,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[801]) ).

thf(443,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__less_0) ).

thf(2396,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(271,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(2015,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(1093,axiom,
    ! [B: $i,A: $i] :
      ( ( c_SetInterval_Oord__class_OatLeastLessThan @ ( hAPP @ c_Suc @ A ) @ B @ tc_nat )
      = ( c_SetInterval_Oord__class_OgreaterThanLessThan @ A @ B @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastSucLessThan__greaterThanLessThan_0) ).

thf(3889,plain,
    ! [B: $i,A: $i] :
      ( ( c_SetInterval_Oord__class_OatLeastLessThan @ ( hAPP @ c_Suc @ A ) @ B @ tc_nat )
      = ( c_SetInterval_Oord__class_OgreaterThanLessThan @ A @ B @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1093]) ).

thf(915,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__add_0) ).

thf(3471,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(835,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).

thf(3286,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(210,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).

thf(1883,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(1060,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OZseq @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_SEQ_OZseq @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__mult__left_0) ).

thf(3810,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OZseq @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_SEQ_OZseq @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1060]) ).

thf(228,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ A ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).

thf(1920,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ A ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(963,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ D ) ) @ B ) ) @ C )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_0) ).

thf(3578,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ D ) ) @ B ) ) @ C )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[963]) ).

thf(654,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).

thf(2872,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(1088,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).

thf(3877,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1088]) ).

thf(1222,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osums @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
      | ~ ( c_Series_Osums @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Osums_0) ).

thf(4187,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osums @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
      | ~ ( c_Series_Osums @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1222]) ).

thf(773,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

thf(3144,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[773]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).

thf(1656,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(412,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).

thf(2327,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(1026,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__commute_0) ).

thf(3727,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(97,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

thf(1634,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(888,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).

thf(3408,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(556,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__decreasing_0) ).

thf(2653,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(691,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).

thf(2958,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).

thf(1120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__add_0) ).

thf(3948,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1120]) ).

thf(845,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ocont_0) ).

thf(3307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(782,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I4_J_0) ).

thf(3166,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(1124,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).

thf(3958,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1124]) ).

thf(1269,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ v_i ) @ A ) @ tc_nat ) @ v_n ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_i__diff_0) ).

thf(4295,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ v_i ) @ A ) @ tc_nat ) @ v_n ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1269]) ).

thf(794,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ C ) @ D @ B @ A @ A ) ) @ E )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ D ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__addf_0) ).

thf(3191,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ C ) @ D @ B @ A @ A ) ) @ E )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ D ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[794]) ).

thf(473,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(2464,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(237,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(1938,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(1134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Series_Osums @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Osums_0) ).

thf(3980,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Series_Osums @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1134]) ).

thf(190,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( c_HOL_Oone__class_Oone @ A ) )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__1_0) ).

thf(1837,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( c_HOL_Oone__class_Oone @ A ) )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(1401,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).

thf(4585,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1401]) ).

thf(459,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add1_0) ).

thf(2433,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(886,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Odistrib__lattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).

thf(3403,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Odistrib__lattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(250,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_5) ).

thf(1968,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(748,axiom,
    ! [A: $i] :
      ( ( hAPP @ c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).

thf(3090,plain,
    ! [A: $i] :
      ( ( hAPP @ c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(797,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

thf(3198,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[797]) ).

thf(1209,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ C ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ D ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Osetsum_0) ).

thf(4155,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ C ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ D ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1209]) ).

thf(630,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib2_0) ).

thf(2820,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(840,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__Suc_0) ).

thf(3297,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[840]) ).

thf(1035,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__field @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) ) @ F )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ E ) ) @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ F ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).

thf(3750,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__field @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) ) @ F )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ E ) ) @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ F ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1035]) ).

thf(181,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

thf(1819,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(93,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).

thf(1624,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(354,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).

thf(2200,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(537,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).

thf(2609,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( hBOOL @ ( hAPP @ C @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(1317,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( hAPP @ c_Suc @ C ) @ D @ tc_nat ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__head__upt__Suc_0) ).

thf(4402,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( hAPP @ c_Suc @ C ) @ D @ tc_nat ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1317]) ).

thf(942,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff__inverse_0) ).

thf(3535,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[942]) ).

thf(346,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_2) ).

thf(2181,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(729,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).

thf(3050,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).

thf(421,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_9) ).

thf(2345,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(509,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).

thf(2547,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(405,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_5) ).

thf(2313,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(1188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ A ) @ A @ A @ A ) @ B ) @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ocont_0) ).

thf(4104,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( c_HOL_Otimes__class_Otimes @ A ) @ A @ A @ A ) @ B ) @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1188]) ).

thf(992,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ F ) @ G ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ G @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__mult_0) ).

thf(3647,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ F ) @ G ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ G @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[992]) ).

thf(1179,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).

thf(4080,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1179]) ).

thf(970,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult_0) ).

thf(3595,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(1155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).

thf(4027,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
      = ( c_Set_Oinsert @ A @ B @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1155]) ).

thf(1279,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F )
      = ( hAPP @ D @ ( hAPP @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).

thf(4316,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F )
      = ( hAPP @ D @ ( hAPP @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1279]) ).

thf(257,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).

thf(1983,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(919,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).

thf(3482,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(622,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_1) ).

thf(2801,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(170,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).

thf(1794,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(174,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).

thf(1804,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(251,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
       != ( c_HOL_Oone__class_Oone @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).

thf(1970,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
       != ( c_HOL_Oone__class_Oone @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(198,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).

thf(1856,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(935,axiom,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
    = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__1__iff_2) ).

thf(3518,plain,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
    = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(1239,axiom,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

thf(4227,plain,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1239]) ).

thf(549,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(2638,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(1236,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ D ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ D @ tc_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sumr__offset3_0) ).

thf(4219,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ D ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ D @ tc_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1236]) ).

thf(709,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ C ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__diff__const_0) ).

thf(3001,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ C ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).

thf(1128,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).

thf(3968,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1128]) ).

thf(375,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).

thf(2245,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(236,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).

thf(1936,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(913,axiom,
    class_Nat_Osemiring__char__0 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).

thf(3467,plain,
    class_Nat_Osemiring__char__0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[913]) ).

thf(79,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).

thf(1592,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(978,axiom,
    class_Lattices_Olower__semilattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).

thf(3615,plain,
    class_Lattices_Olower__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[978]) ).

thf(58,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(1541,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(335,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__le__iff_0) ).

thf(2157,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(640,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OLIMSEQ @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ C @ E @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__mult_0) ).

thf(2840,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OLIMSEQ @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ C @ E @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(1190,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).

thf(4108,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1190]) ).

thf(1354,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osums @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_Series_Osums @ C @ E @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__add_0) ).

thf(4486,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osums @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_Series_Osums @ C @ E @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1354]) ).

thf(39,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).

thf(1498,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(77,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).

thf(1587,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(492,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

thf(2509,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(753,axiom,
    class_Orderings_Obot @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).

thf(3102,plain,
    class_Orderings_Obot @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[753]) ).

thf(1017,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ C )
        = ( c_Series_Osuminf @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A ) )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Osuminf_0) ).

thf(3704,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ C )
        = ( c_Series_Osuminf @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A ) )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(589,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_0) ).

thf(2726,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(546,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

thf(2631,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(761,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).

thf(3119,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(1033,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).

thf(3746,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(994,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).

thf(3650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(1149,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc2_0) ).

thf(4012,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1149]) ).

thf(1105,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__vector @ B )
      | ( c_Lim_OisCont @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ B @ B ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ B ) ) @ C ) @ D @ A @ B @ B ) @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ D @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ C @ E @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__add_0) ).

thf(3916,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__vector @ B )
      | ( c_Lim_OisCont @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ B @ B ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ B ) ) @ C ) @ D @ A @ B @ B ) @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ D @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ C @ E @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1105]) ).

thf(151,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).

thf(1755,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(733,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ C ) ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ D ) ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__realpow__diff_0) ).

thf(3060,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ C ) ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ D ) ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(786,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_0) ).

thf(3176,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[786]) ).

thf(847,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).

thf(3311,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[847]) ).

thf(1075,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).

thf(3846,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1075]) ).

thf(982,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

thf(3622,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[982]) ).

thf(635,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

thf(2830,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(652,axiom,
    class_Lattices_Obounded__lattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).

thf(2868,plain,
    class_Lattices_Obounded__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(1224,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).

thf(4191,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1224]) ).

thf(128,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).

thf(1700,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(1002,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

thf(3671,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1002]) ).

thf(961,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_0) ).

thf(3573,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(613,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ D ) ) ) @ tc_nat @ A @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ c_Suc @ D ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) ) @ tc_nat @ A @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ c_Suc @ D ) @ tc_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__realpow__diff__sumr_0) ).

thf(2781,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__0 @ A )
      | ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ D ) ) ) @ tc_nat @ A @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ c_Suc @ D ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) ) @ tc_nat @ A @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ c_Suc @ D ) @ tc_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(69,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_3) ).

thf(1567,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(1267,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_1) ).

thf(4291,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1267]) ).

thf(1281,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ c_Suc @ B ) )
      = ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__Suc__right_0) ).

thf(4320,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ c_Suc @ B ) )
      = ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1281]) ).

thf(621,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

thf(2798,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(1122,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_2) ).

thf(3954,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1122]) ).

thf(1164,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).

thf(4049,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1164]) ).

thf(1272,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).

thf(4301,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1272]) ).

thf(275,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).

thf(2023,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_8) ).

thf(1942,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(1259,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) )
      | ( D
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).

thf(4276,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) )
      | ( D
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1259]) ).

thf(410,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_4) ).

thf(2323,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(788,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).

thf(3179,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(1213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).

thf(4167,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1213]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(1739,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(22,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).

thf(1461,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(1328,axiom,
    ! [A: $i] :
      ( ( ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
        = A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__pred_0) ).

thf(4425,plain,
    ! [A: $i] :
      ( ( ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) )
        = A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1328]) ).

thf(5,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).

thf(1424,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(902,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ C ) ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ C ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_0) ).

thf(3441,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ C ) ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ C ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(470,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).

thf(2455,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(1381,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__less__cancel1_1) ).

thf(4545,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1381]) ).

thf(302,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(2080,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(1,negated_conjecture,
    ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ v_i ) ) ) ) @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) ) ) @ v_a @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ v_i @ v_n @ tc_nat ) )
   != ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ v_i ) ) ) ) @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) ) ) @ v_a @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ v_i @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_nat ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ v_i @ v_n @ tc_nat ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(1414,plain,
    ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ v_i ) ) ) ) @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) ) ) @ v_a @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ v_i @ v_n @ tc_nat ) )
   != ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ v_i ) ) ) ) @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) ) ) @ v_a @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ v_i @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_nat ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ v_i @ v_n @ tc_nat ) @ ( tc_fun @ tc_nat @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(289,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).

thf(2053,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(192,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_1) ).

thf(1842,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_0) ).

thf(2172,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(1166,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__pwr_0) ).

thf(4054,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1166]) ).

thf(896,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).

thf(3428,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ E ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[896]) ).

thf(795,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__mult_0) ).

thf(3194,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(423,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( B = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(2349,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( B = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).

thf(2038,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(15,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
        = B )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_3) ).

thf(1446,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
        = B )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(213,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).

thf(1889,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(952,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OLIM__zero_0) ).

thf(3555,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[952]) ).

thf(1341,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).

thf(4457,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1341]) ).

thf(88,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).

thf(1612,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(477,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

thf(2472,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(407,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_6) ).

thf(2317,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(146,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ B @ C @ A )
      | ~ ( c_Deriv_Oderiv @ B @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__def_1) ).

thf(1744,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ B @ C @ A )
      | ~ ( c_Deriv_Oderiv @ B @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(817,axiom,
    ! [A: $i] :
      ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan0_0) ).

thf(3242,plain,
    ! [A: $i] :
      ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(996,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).

thf(3656,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

thf(17,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).

thf(1451,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(484,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

thf(2487,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(1032,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).

thf(3743,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).

thf(374,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).

thf(2243,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(241,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).

thf(1947,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(984,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).

thf(3628,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Olattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).

thf(136,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).

thf(1720,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(432,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).

thf(2370,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(1016,axiom,
    class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).

thf(3703,plain,
    class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1016]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(1825,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(695,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).

thf(2968,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(393,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_4) ).

thf(2285,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(921,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) ) @ D ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OLIM__zero_0) ).

thf(3486,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) ) @ D ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[921]) ).

thf(322,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

thf(2125,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(503,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_0) ).

thf(2536,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(765,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).

thf(3126,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(568,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).

thf(2681,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).

thf(638,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_3) ).

thf(2836,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(19,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_2) ).

thf(1456,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(1364,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osums @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
      | ~ ( c_Series_Osums @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__mult_0) ).

thf(4508,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osums @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
      | ~ ( c_Series_Osums @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1364]) ).

thf(866,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).

thf(3354,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(439,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ E @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less2_0) ).

thf(2387,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ E @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(187,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).

thf(1831,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(234,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__le_0) ).

thf(1932,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(1246,axiom,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
    = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_5) ).

thf(4244,plain,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
    = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1246]) ).

thf(807,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).

thf(3222,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(268,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).

thf(2006,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(488,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

thf(2497,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(1379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_1) ).

thf(4540,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1379]) ).

thf(944,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).

thf(3540,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(196,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_3) ).

thf(1852,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(627,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).

thf(2813,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(1039,axiom,
    class_Nat_Osemiring__char__0 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Nat_Osemiring__char__0) ).

thf(3760,plain,
    class_Nat_Osemiring__char__0 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1039]) ).

thf(819,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

thf(3247,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[819]) ).

thf(82,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).

thf(1599,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(576,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ tc_nat @ A @ A ) @ D ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sumr__diff__mult__const2_0) ).

thf(2697,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ tc_nat @ A @ A ) @ D ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(134,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) ) @ C )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_3) ).

thf(1715,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) ) @ C )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(856,axiom,
    class_Orderings_Opreorder @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).

thf(3333,plain,
    class_Orderings_Opreorder @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(756,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__iff_0) ).

thf(3109,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(255,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).

thf(1979,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(741,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oinverse__class_Odivide @ A ) @ A @ A @ A ) @ B ) @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ocont_0) ).

thf(3074,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oinverse__class_Odivide @ A ) @ A @ A @ A ) @ B ) @ C @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).

thf(1324,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) )
      | ( B = D )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__imp__eq__base_0) ).

thf(4416,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) )
      | ( B = D )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1324]) ).

thf(1107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

thf(3920,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1107]) ).

thf(387,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_2) ).

thf(2272,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(328,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ B )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).

thf(2140,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ B )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(1181,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_1) ).

thf(4086,plain,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1181]) ).

thf(602,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff_0) ).

thf(2756,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(745,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ tc_nat @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ A ) ) @ B ) @ A @ tc_nat @ A ) @ C ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ) ) @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__power_0) ).

thf(3083,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ tc_nat @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ A ) ) @ B ) @ A @ tc_nat @ A ) @ C ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ B @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ) ) @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(780,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).

thf(3162,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[780]) ).

thf(798,axiom,
    ( ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_4) ).

thf(3201,plain,
    ( ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(153,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).

thf(1759,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(774,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_2) ).

thf(3147,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(163,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).

thf(1779,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(358,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(2208,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(1232,axiom,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_2) ).

thf(4212,plain,
    ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1232]) ).

thf(126,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_5) ).

thf(1695,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(1079,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ A ) ) @ B ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__summation_0) ).

thf(3856,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ A ) ) @ B ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1079]) ).

thf(693,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_Series_Osuminf @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ C ) )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_suminf__divide_0) ).

thf(2963,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_Series_Osuminf @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ C ) )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).

thf(1466,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(47,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( B = C )
      | ~ ( c_Deriv_Oderiv @ D @ E @ C @ A )
      | ~ ( c_Deriv_Oderiv @ D @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__unique_0) ).

thf(1515,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( B = C )
      | ~ ( c_Deriv_Oderiv @ D @ E @ C @ A )
      | ~ ( c_Deriv_Oderiv @ D @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(216,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_8) ).

thf(1895,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(560,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).

thf(2662,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(1393,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__diff__conv_1) ).

thf(4572,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1393]) ).

thf(1066,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).

thf(3824,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1066]) ).

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

thf(2634,plain,
    class_Ring__and__Field_Opordered__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(599,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__zero_0) ).

thf(2749,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(1099,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ c_Suc @ B ) ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__less_0) ).

thf(3903,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ c_Suc @ B ) ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1099]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).

thf(1991,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(616,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).

thf(2788,plain,
    class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(1070,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) @ D ) )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__num__frac_0) ).

thf(3834,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) @ D ) )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1070]) ).

thf(1265,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ A )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self__eq__0_0) ).

thf(4288,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ A )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1265]) ).

thf(604,axiom,
    class_Power_Opower @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).

thf(2761,plain,
    class_Power_Opower @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(785,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( c_HOL_Oinverse__class_Oinverse @ A ) ) @ C ) @ D @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ E ) @ B @ A )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Lim_OLIM @ C @ D @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__inverse_0) ).

thf(3173,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( c_HOL_Oinverse__class_Oinverse @ A ) ) @ C ) @ D @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ E ) @ B @ A )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Lim_OLIM @ C @ D @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(1350,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).

thf(4476,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1350]) ).

thf(988,axiom,
    class_Ring__and__Field_Ozero__neq__one @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

thf(3639,plain,
    class_Ring__and__Field_Ozero__neq__one @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

thf(672,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Limits_Otendsto @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ E ) @ D ) @ F @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ E @ F @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Otendsto_0) ).

thf(2915,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Limits_Otendsto @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ E ) @ D ) @ F @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ E @ F @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(463,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).

thf(2440,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(448,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).

thf(2408,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(619,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ E ) @ D ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ D ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ E @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__shift__bounds__nat__ivl_0) ).

thf(2793,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ E ) @ D ) @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ D ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ E @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(553,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__exp_0) ).

thf(2645,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(894,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__empty_0) ).

thf(3422,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[894]) ).

thf(1004,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

thf(3675,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(1276,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).

thf(4308,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1276]) ).

thf(454,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).

thf(2423,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(500,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_3) ).

thf(2529,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(591,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__idem_0) ).

thf(2729,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(266,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ( ( c_HOL_Oone__class_Oone @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

thf(2001,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ( ( c_HOL_Oone__class_Oone @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(344,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).

thf(2176,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(441,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_0) ).

thf(2391,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(232,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).

thf(1927,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(1389,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__mult__distrib2_0) ).

thf(4562,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1389]) ).

thf(1362,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__self__zero_0) ).

thf(4503,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1362]) ).

thf(757,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ E ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Osetsum_0) ).

thf(3111,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ E ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(96,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).

thf(1631,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(320,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__mono1_0) ).

thf(2121,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(370,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_1) ).

thf(2235,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(1018,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__diff_0) ).

thf(3707,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(45,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OisCont @ C @ D @ A @ B )
      | ~ ( c_Lim_OLIM @ C @ D @ ( hAPP @ C @ D ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__def_1) ).

thf(1510,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OisCont @ C @ D @ A @ B )
      | ~ ( c_Lim_OLIM @ C @ D @ ( hAPP @ C @ D ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(396,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_0) ).

thf(2292,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(1308,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).

thf(4380,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( A = E )
      | ( B = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1308]) ).

thf(246,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).

thf(1959,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(513,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(2556,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(379,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( c_Series_Osummable @ B @ A )
      | ( c_Series_Osums @ B @ ( c_Series_Osuminf @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__iff_2) ).

thf(2253,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( c_Series_Osummable @ B @ A )
      | ( c_Series_Osums @ B @ ( c_Series_Osuminf @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(332,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

thf(2149,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(923,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ~ ( class_RealVector_Ometric__space @ C )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F @ ( hAPP @ D @ G ) @ C @ B )
      | ~ ( c_Lim_OLIM @ E @ F @ G @ C @ A )
      | ~ ( c_Lim_OisCont @ D @ G @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__LIM__compose_0) ).

thf(3491,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ~ ( class_RealVector_Ometric__space @ C )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F @ ( hAPP @ D @ G ) @ C @ B )
      | ~ ( c_Lim_OLIM @ E @ F @ G @ C @ A )
      | ~ ( c_Lim_OisCont @ D @ G @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[923]) ).

thf(32,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_3) ).

thf(1483,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(743,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).

thf(3079,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(1321,axiom,
    class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

thf(4412,plain,
    class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1321]) ).

thf(1251,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing_0) ).

thf(4256,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1251]) ).

thf(1030,axiom,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).

thf(3738,plain,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(1291,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).

thf(4340,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1291]) ).

thf(875,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).

thf(3375,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_1) ).

thf(1595,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(1072,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

thf(3839,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Oone__class_Oone @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1072]) ).

thf(937,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).

thf(3523,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[937]) ).

thf(1256,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OgreaterThanLessThan @ B @ D @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I15_J_0) ).

thf(4269,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OgreaterThanLessThan @ B @ D @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1256]) ).

thf(1009,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osums @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_Series_Osums @ C @ E @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__diff_0) ).

thf(3686,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osums @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) @ A )
      | ~ ( c_Series_Osums @ C @ E @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1009]) ).

thf(1151,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_OZfun @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ D @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ C @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__mult_0) ).

thf(4017,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_OZfun @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ D @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ C @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1151]) ).

thf(663,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).

thf(2894,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(1301,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_OZfun @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) ) @ D ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ D @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OZfun_0) ).

thf(4365,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_OZfun @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) ) @ D ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ D @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1301]) ).

thf(883,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).

thf(3396,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(435,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( B = C )
      | ~ ( c_SEQ_OLIMSEQ @ D @ C @ A )
      | ~ ( c_SEQ_OLIMSEQ @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__unique_0) ).

thf(2376,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( B = C )
      | ~ ( c_SEQ_OLIMSEQ @ D @ C @ A )
      | ~ ( c_SEQ_OLIMSEQ @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(860,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).

thf(3343,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(778,axiom,
    ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) ) @ ( c_COMBS @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ tc_nat ) @ ( c_HOL_OIf @ tc_Complex_Ocomplex ) ) @ ( c_lessequals @ v_i @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ v_i ) ) @ tc_nat @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ tc_Complex_Ocomplex ) @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) ) ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ v_i ) ) @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) ) @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) ) ) @ v_a @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) )
    = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ v_i ) ) ) ) @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) ) ) @ v_a @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ v_i @ v_n @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_calculation_0) ).

thf(3158,plain,
    ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) ) @ ( c_COMBS @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_bool @ ( tc_fun @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ tc_nat ) @ ( c_HOL_OIf @ tc_Complex_Ocomplex ) ) @ ( c_lessequals @ v_i @ tc_nat ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ v_i ) ) @ tc_nat @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ tc_Complex_Ocomplex ) @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) ) ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ v_i ) ) @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) ) @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) ) ) @ v_a @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) )
    = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ ( tc_fun @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_nat @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ v_n ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ v_i ) ) ) ) @ tc_nat @ ( tc_fun @ tc_nat @ tc_bool ) @ tc_Complex_Ocomplex ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ v_n @ tc_nat ) ) ) @ v_a @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ v_i @ v_n @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[778]) ).

thf(851,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ D ) ) @ B ) ) @ C ) ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__add__eq1_0) ).

thf(3319,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ D ) ) @ B ) ) @ C ) ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(617,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).

thf(2789,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(349,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

thf(2188,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(91,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).

thf(1620,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(833,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_0) ).

thf(3283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(249,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__inverse_0) ).

thf(1965,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(633,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).

thf(2827,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(1205,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

thf(4144,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1205]) ).

thf(874,axiom,
    ! [A: $i] :
      ( ( hAPP @ c_Suc @ A )
     != A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).

thf(3372,plain,
    ! [A: $i] :
      ( ( hAPP @ c_Suc @ A )
     != A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(1143,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ v_i ) @ tc_nat ) @ v_n ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ v_n ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__i_0) ).

thf(4000,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ v_i ) @ tc_nat ) @ v_n ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ v_n ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1143]) ).

thf(792,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).

thf(3187,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[792]) ).

thf(948,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel2_1) ).

thf(3547,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[948]) ).

thf(188,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).

thf(1833,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(987,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ E )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).

thf(3636,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ E )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(287,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).

thf(2048,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(1109,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) @ E ) ) @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).

thf(3925,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) @ E ) ) @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1109]) ).

thf(648,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__conv_1) ).

thf(2859,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(682,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OLIMSEQ_0) ).

thf(2938,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(1262,axiom,
    class_Ring__and__Field_Oordered__semiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

thf(4283,plain,
    class_Ring__and__Field_Oordered__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1262]) ).

thf(165,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).

thf(1784,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(1178,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

thf(4077,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1178]) ).

thf(618,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ A @ A @ A ) @ ( hAPP @ B @ C ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Ominus__class_Ominus @ A ) @ A @ A @ A ) @ C ) @ A @ A @ A ) @ C @ D @ A @ A )
      | ~ ( c_Deriv_Oderiv @ B @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__iff2_0) ).

thf(2791,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ A @ A @ A ) @ ( hAPP @ B @ C ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Ominus__class_Ominus @ A ) @ A @ A @ A ) @ C ) @ A @ A @ A ) @ C @ D @ A @ A )
      | ~ ( c_Deriv_Oderiv @ B @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(816,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).

thf(3240,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Obot @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(558,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_0) ).

thf(2657,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).

thf(644,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ tc_nat @ A @ A ) ) @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ D @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) ) @ tc_nat @ A @ A ) @ tc_nat @ A @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ D @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__termdiff1_0) ).

thf(2849,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ tc_nat @ A @ A ) ) @ tc_nat @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ D @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) ) @ tc_nat @ A @ A ) @ tc_nat @ A @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ D @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(442,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__distrib__number__of_0) ).

thf(2393,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(150,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_2) ).

thf(1752,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(105,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

thf(1652,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(744,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_1) ).

thf(3081,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).

thf(1119,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I11_J_0) ).

thf(3945,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1119]) ).

thf(829,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).

thf(3272,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(1196,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Series_Osums @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__divide_0) ).

thf(4122,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Series_Osums @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1196]) ).

thf(624,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_OLIM__zero_0) ).

thf(2806,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(705,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ D @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ C ) @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sumr__offset_0) ).

thf(2991,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ D @ tc_nat ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ D ) @ C ) @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).

thf(444,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).

thf(2398,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(1285,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__0_0) ).

thf(4328,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1285]) ).

thf(1403,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__ignore__initial__segment_0) ).

thf(4590,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1403]) ).

thf(1084,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).

thf(3868,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1084]) ).

thf(1411,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) @ A ) @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).

thf(4612,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ E ) ) @ C ) ) @ D ) @ A ) @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1411]) ).

thf(575,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ B @ D ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ F ) @ ( hAPP @ C @ D ) ) ) @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ E @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ F @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__mult_H_0) ).

thf(2695,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ B @ D ) ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ F ) @ ( hAPP @ C @ D ) ) ) @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ E @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ F @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).

thf(34,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less__one_0) ).

thf(1488,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(278,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).

thf(2029,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(1192,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).

thf(4112,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1192]) ).

thf(1322,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel2_1) ).

thf(4413,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1322]) ).

thf(763,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C ) ) @ D ) @ tc_nat ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ D ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_0) ).

thf(3123,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C ) ) @ D ) @ tc_nat ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ D ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(1015,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) )
        = B )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).

thf(3700,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) )
        = B )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).

thf(1897,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(455,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I3_J_0) ).

thf(2425,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(844,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_0) ).

thf(3304,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(478,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).

thf(2474,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(99,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).

thf(1638,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(116,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).

thf(1675,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(941,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).

thf(3532,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_8) ).

thf(1428,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(808,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B )
        = ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__le_0) ).

thf(3223,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B )
        = ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[808]) ).

thf(337,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_1) ).

thf(2161,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(1372,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ A )
      | ( ( hAPP @ C @ D )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Deriv_Odifferentiable @ C @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__divide_0) ).

thf(4526,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ A )
      | ( ( hAPP @ C @ D )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Deriv_Odifferentiable @ C @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1372]) ).

thf(1377,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D ) ) @ E ) @ A ) @ F ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).

thf(4537,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D ) ) @ E ) @ A ) @ F ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1377]) ).

thf(1387,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).

thf(4558,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1387]) ).

thf(113,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).

thf(1669,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(351,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).

thf(2193,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(166,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_9) ).

thf(1786,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(1198,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).

thf(4127,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1198]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(2220,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(1126,axiom,
    class_Ring__and__Field_Ocomm__ring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).

thf(3964,plain,
    class_Ring__and__Field_Ocomm__ring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1126]) ).

thf(1013,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ C ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__cancel1_0) ).

thf(3695,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ C ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(1186,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C )
        = B )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).

thf(4099,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ C )
        = B )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1186]) ).

thf(855,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__is__0__eq_0) ).

thf(3330,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[855]) ).

thf(1215,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).

thf(4171,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1215]) ).

thf(202,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ B @ C @ A )
      | ~ ( c_Deriv_Oderiv @ B @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiableI_0) ).

thf(1865,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ B @ C @ A )
      | ~ ( c_Deriv_Oderiv @ B @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(681,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_1) ).

thf(2935,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).

thf(141,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

thf(1733,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(859,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ ( c_Series_Osuminf @ C @ A ) )
        = ( c_Series_Osuminf @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A ) )
      | ~ ( c_Series_Osummable @ C @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_suminf__add_0) ).

thf(3340,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ ( c_Series_Osuminf @ C @ A ) )
        = ( c_Series_Osuminf @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A ) )
      | ~ ( c_Series_Osummable @ C @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(264,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).

thf(1997,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(464,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_0) ).

thf(2442,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(603,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).

thf(2759,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).

thf(1049,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Limits_Otendsto @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ D @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ F ) @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ D @ F @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ E @ G @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__diff_0) ).

thf(3783,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Limits_Otendsto @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ D @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ F ) @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ D @ F @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ E @ G @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1049]) ).

thf(290,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).

thf(2055,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(1069,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A )
      | ~ ( c_Series_Osummable @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Osummable_0) ).

thf(3832,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A )
      | ~ ( c_Series_Osummable @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1069]) ).

thf(339,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ B ) @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).

thf(2166,plain,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ B ) @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(156,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).

thf(1765,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(843,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).

thf(3302,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[843]) ).

thf(959,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).

thf(3568,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(1023,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).

thf(3719,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

thf(427,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_5) ).

thf(2358,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(408,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_1) ).

thf(2319,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(1331,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).

thf(4433,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1331]) ).

thf(1006,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ tc_nat ) ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ E @ tc_nat ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__add__nat__ivl_0) ).

thf(3678,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ E @ tc_nat ) ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ E @ tc_nat ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1006]) ).

thf(404,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).

thf(2311,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(497,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).

thf(2521,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(319,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__less__add2_0) ).

thf(2119,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(950,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__mult__left__zero_0) ).

thf(3551,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(175,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).

thf(1806,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(1047,axiom,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).

thf(3779,plain,
    ! [A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1047]) ).

thf(828,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).

thf(3270,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(1413,axiom,
    class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).

thf(4616,plain,
    class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1413]) ).

thf(1240,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ B @ C @ D @ A )
      | ~ ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ A @ A @ A ) @ ( hAPP @ B @ C ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Ominus__class_Ominus @ A ) @ A @ A @ A ) @ C ) @ A @ A @ A ) @ C @ D @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__iff2_1) ).

thf(4228,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ B @ C @ D @ A )
      | ~ ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ A @ A @ A ) @ ( hAPP @ B @ C ) ) ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Ominus__class_Ominus @ A ) @ A @ A @ A ) @ C ) @ A @ A @ A ) @ C @ D @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1240]) ).

thf(504,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__Suc__add_1) ).

thf(2538,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(1359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__divide_0) ).

thf(4498,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Series_Osummable @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1359]) ).

thf(1303,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).

thf(4369,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1303]) ).

thf(777,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

thf(3155,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(367,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).

thf(2229,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(1063,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ B )
        = A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse2_0) ).

thf(3815,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ B )
        = A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1063]) ).

thf(815,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mult__le__cancel1_1) ).

thf(3238,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(361,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).

thf(2214,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(1041,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).

thf(3764,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1041]) ).

thf(451,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
       != ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_0) ).

thf(2415,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
       != ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(486,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).

thf(2493,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(51,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).

thf(1524,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(934,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ ( hAPP @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ B @ D ) ) @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ D ) ) ) @ A )
      | ( ( hAPP @ C @ D )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__divide_0) ).

thf(3515,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ ( hAPP @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ B @ D ) ) @ F ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ C @ D ) ) ) @ A )
      | ( ( hAPP @ C @ D )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(1028,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).

thf(3732,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(381,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).

thf(2257,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(78,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

thf(1589,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(36,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__0__iff_0) ).

thf(1492,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(84,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_7) ).

thf(1603,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(399,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_6) ).

thf(2299,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(1407,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).

thf(4601,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1407]) ).

thf(755,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

thf(3106,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[755]) ).

thf(914,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__eq__cancel1_0) ).

thf(3468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(318,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).

thf(2116,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(639,axiom,
    class_Ring__and__Field_Osemiring__1 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).

thf(2839,plain,
    class_Ring__and__Field_Osemiring__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).

thf(159,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).

thf(1771,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(684,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Lim_OisCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OisCont_0) ).

thf(2943,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Lim_OisCont @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(1019,axiom,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).

thf(3710,plain,
    ! [A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(685,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__mult__zero_0) ).

thf(2945,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).

thf(647,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Odiff_0) ).

thf(2856,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(927,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).

thf(3500,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(770,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).

thf(3138,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[770]) ).

thf(966,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
      | ( c_Lim_OLIM @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__inverse__fun_0) ).

thf(3586,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
      | ( c_Lim_OLIM @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(123,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).

thf(1690,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(790,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel2_2) ).

thf(3182,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[790]) ).

thf(735,axiom,
    class_Ring__and__Field_Osemiring__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1) ).

thf(3066,plain,
    class_Ring__and__Field_Osemiring__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(664,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I1_J_0) ).

thf(2896,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatMost @ B @ A ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(2197,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( C = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(779,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ F ) @ D ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_OLIM_0) ).

thf(3160,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ B @ A @ A ) @ D ) @ E @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ F ) @ D ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(295,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).

thf(2065,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(1311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).

thf(4388,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1311]) ).

thf(112,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(1667,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(1330,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ D ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(4430,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ D ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1330]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).

thf(1877,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(276,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_4) ).

thf(2025,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(719,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ tc_nat ) @ ( c_Finite__Set_Osetsum @ B @ A ) ) @ ( c_COMBC @ C @ B @ tc_nat @ A ) ) @ tc_nat @ ( tc_fun @ B @ tc_bool ) @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ E ) @ D ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ ( hAPP @ C @ ( c_SEQ_Osko__SEQ__XLIMSEQ__setsum__1__1 @ E @ D @ C @ B @ A ) ) @ ( hAPP @ E @ ( c_SEQ_Osko__SEQ__XLIMSEQ__setsum__1__1 @ E @ D @ C @ B @ A ) ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__setsum_1) ).

thf(3027,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ B @ A ) @ ( tc_fun @ ( tc_fun @ B @ tc_bool ) @ A ) @ tc_nat ) @ ( c_Finite__Set_Osetsum @ B @ A ) ) @ ( c_COMBC @ C @ B @ tc_nat @ A ) ) @ tc_nat @ ( tc_fun @ B @ tc_bool ) @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ E ) @ D ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ ( hAPP @ C @ ( c_SEQ_Osko__SEQ__XLIMSEQ__setsum__1__1 @ E @ D @ C @ B @ A ) ) @ ( hAPP @ E @ ( c_SEQ_Osko__SEQ__XLIMSEQ__setsum__1__1 @ E @ D @ C @ B @ A ) ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(1392,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).

thf(4569,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1392]) ).

thf(385,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).

thf(2267,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(466,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel__le_1) ).

thf(2446,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(1287,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_0) ).

thf(4332,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1287]) ).

thf(711,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).

thf(3006,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).

thf(1270,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

thf(4296,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1270]) ).

thf(1081,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Lim_OisCont @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oinverse__class_Odivide @ A ) @ A @ A @ A ) @ B ) @ C @ A @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_OisCont_0) ).

thf(3861,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Lim_OisCont @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oinverse__class_Odivide @ A ) @ A @ A @ A ) @ B ) @ C @ A @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1081]) ).

thf(390,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(2278,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(806,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

thf(3219,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[806]) ).

thf(632,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( c_Series_Osums @ B @ C @ A )
      | ~ ( c_Series_Osums @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ c_Suc ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__Suc__imp_0) ).

thf(2824,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( c_Series_Osums @ B @ C @ A )
      | ~ ( c_Series_Osums @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ c_Suc ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).

thf(768,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).

thf(3133,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[768]) ).

thf(731,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).

thf(3055,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(420,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).

thf(2343,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(543,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).

thf(2625,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(1343,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ c_Suc ) @ C @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__Suc_0) ).

thf(4462,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ c_Suc ) @ C @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1343]) ).

thf(316,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).

thf(2111,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(740,axiom,
    class_Lattices_Odistrib__lattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).

thf(3073,plain,
    class_Lattices_Odistrib__lattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).

thf(1171,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__decreasing_0) ).

thf(4064,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1171]) ).

thf(262,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1_0) ).

thf(1993,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(182,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

thf(1821,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(140,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).

thf(1731,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(1254,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_Power_Opower @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ tc_nat @ A ) @ tc_nat ) @ ( c_Power_Opower__class_Opower @ A ) ) @ B ) @ tc_nat @ tc_nat @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__pow_0) ).

thf(4264,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_Power_Opower @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ tc_nat @ A ) @ tc_nat ) @ ( c_Power_Opower__class_Opower @ A ) ) @ B ) @ tc_nat @ tc_nat @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1254]) ).

thf(1112,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
      = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__commute_0) ).

thf(3932,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
      = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1112]) ).

thf(223,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).

thf(1909,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
       != ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_1) ).

thf(1862,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
       != ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(1219,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).

thf(4181,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1219]) ).

thf(722,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_1) ).

thf(3034,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(449,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).

thf(2410,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(675,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ A ) @ C ) @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ C @ D ) @ A @ B )
      | ~ ( c_Lim_OLIM @ C @ D @ ( hAPP @ C @ D ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__isCont__iff_0) ).

thf(2923,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ A ) @ C ) @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ C @ D ) @ A @ B )
      | ~ ( c_Lim_OLIM @ C @ D @ ( hAPP @ C @ D ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(1129,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

thf(3971,plain,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1129]) ).

thf(965,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).

thf(3583,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( C = B )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(1556,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( C = B )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(21,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__ex__iff_1) ).

thf(1460,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(554,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ D ) )
      | ( C
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) @ A ) ) @ B ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff2_0) ).

thf(2647,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ D ) )
      | ( C
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ D ) @ A ) ) @ B ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(472,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add__meet @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) @ D )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__inf__distrib__right_0) ).

thf(2461,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add__meet @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) @ D )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(697,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

thf(2974,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(413,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_2) ).

thf(2329,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(641,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__algebra @ B )
      | ( c_Lim_OisCont @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ B @ B ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B ) ) @ C ) @ D @ A @ B @ B ) @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ D @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ C @ E @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__mult_0) ).

thf(2842,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__algebra @ B )
      | ( c_Lim_OisCont @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ B @ B ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ B ) ) @ C ) @ D @ A @ B @ B ) @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ D @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ C @ E @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(243,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).

thf(1952,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(1095,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ C )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

thf(3893,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1095]) ).

thf(581,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).

thf(2710,plain,
    ! [B: $i,A: $i] :
      ( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Lattices_Obounded__lattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(670,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nat_Oadd__0__right_0) ).

thf(2911,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(523,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).

thf(2578,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(122,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).

thf(1688,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(918,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ~ ( class_RealVector_Ometric__space @ C )
      | ( c_Lim_OisCont @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ B @ A ) @ D ) @ E ) @ F @ A @ B )
      | ~ ( c_Lim_OisCont @ D @ ( hAPP @ E @ F ) @ C @ B )
      | ~ ( c_Lim_OisCont @ E @ F @ A @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__o2_0) ).

thf(3480,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ~ ( class_RealVector_Ometric__space @ C )
      | ( c_Lim_OisCont @ ( hAPP @ ( hAPP @ ( c_COMBB @ C @ B @ A ) @ D ) @ E ) @ F @ A @ B )
      | ~ ( c_Lim_OisCont @ D @ ( hAPP @ E @ F ) @ C @ B )
      | ~ ( c_Lim_OisCont @ E @ F @ A @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).

thf(430,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).

thf(2365,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(1242,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I35_J_0) ).

thf(4232,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1242]) ).

thf(360,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_4) ).

thf(2212,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) @ D )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I1_J_0) ).

thf(1528,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) @ D )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(304,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(2086,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(1058,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).

thf(3806,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1058]) ).

thf(679,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Limits_Otendsto @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ C ) @ D @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ E ) @ F ) @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ D @ F @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ E @ G @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__add_0) ).

thf(2931,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Limits_Otendsto @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ C ) @ D @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ E ) @ F ) @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ D @ F @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ E @ G @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(715,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).

thf(3016,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
       != ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
      | ( B = D )
      | ( A = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(870,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

thf(3363,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[870]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).

thf(1726,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(1173,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__assoc2_0) ).

thf(4067,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ C ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1173]) ).

thf(297,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_1) ).

thf(2069,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(300,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
       != ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).

thf(2075,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
       != ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(452,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).

thf(2418,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(588,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).

thf(2725,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).

thf(445,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(2401,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(288,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__increasing__iff_0) ).

thf(2051,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(606,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__diff__is__add_0) ).

thf(2765,plain,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(481,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

thf(2481,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(10,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).

thf(1435,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(161,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).

thf(1775,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(530,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).

thf(2592,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(29,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

thf(1477,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(853,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ D ) ) @ B ) ) @ C ) @ tc_nat ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__add__iff1_1) ).

thf(3325,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ D ) ) @ B ) ) @ C ) @ tc_nat ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[853]) ).

thf(772,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OCauchy @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_SEQ_OCauchy @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OCauchy_0) ).

thf(3142,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OCauchy @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_SEQ_OCauchy @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[772]) ).

thf(311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).

thf(2101,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(1274,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__vector @ B )
      | ( c_Lim_OisCont @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ B @ B ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ B ) ) @ C ) @ D @ A @ B @ B ) @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ D @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ C @ E @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__diff_0) ).

thf(4304,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__vector @ B )
      | ( c_Lim_OisCont @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ B @ B ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ B ) ) @ C ) @ D @ A @ B @ B ) @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ D @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ C @ E @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1274]) ).

thf(38,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

thf(1496,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(401,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( B = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(2303,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( B = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(932,axiom,
    class_Orderings_Obot @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).

thf(3512,plain,
    class_Orderings_Obot @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[932]) ).

thf(787,axiom,
    class_Lattices_Odistrib__lattice @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).

thf(3178,plain,
    class_Lattices_Odistrib__lattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(708,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).

thf(2999,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(864,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).

thf(3348,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(1102,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ E @ A ) @ F ) @ G ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ A ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ E @ A ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_COMBB @ A @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) @ B @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ F ) ) @ B @ ( tc_fun @ E @ tc_bool ) @ A ) @ G ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__product_0) ).

thf(3908,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ E @ A ) @ F ) @ G ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ E @ A ) @ ( tc_fun @ ( tc_fun @ E @ tc_bool ) @ A ) @ B ) @ ( c_Finite__Set_Osetsum @ E @ A ) ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ ( tc_fun @ A @ A ) @ ( tc_fun @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ B ) @ ( c_COMBB @ A @ A @ E ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) ) @ B @ ( tc_fun @ E @ A ) @ ( tc_fun @ E @ A ) ) @ F ) ) @ B @ ( tc_fun @ E @ tc_bool ) @ A ) @ G ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1102]) ).

thf(574,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).

thf(2693,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(1231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ C ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).

thf(4209,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ C ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1231]) ).

thf(702,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_1) ).

thf(2984,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(252,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).

thf(1973,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(1352,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).

thf(4481,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1352]) ).

thf(1210,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).

thf(4158,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1210]) ).

thf(491,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ B )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self_0) ).

thf(2506,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ B )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(1348,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__Suc_0) ).

thf(4473,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1348]) ).

thf(877,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq1_0) ).

thf(3380,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_0) ).

thf(1626,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(372,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_9) ).

thf(2239,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(688,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__cmult__Id_0) ).

thf(2952,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(205,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).

thf(1873,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(561,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq__number__of_3) ).

thf(2665,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(614,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OZseq @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__Zseq__iff_0) ).

thf(2784,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OZseq @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).

thf(1373,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OZseq @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A )
      | ~ ( c_SEQ_OZseq @ C @ A )
      | ~ ( c_SEQ_OZseq @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__add_0) ).

thf(4529,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OZseq @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A )
      | ~ ( c_SEQ_OZseq @ C @ A )
      | ~ ( c_SEQ_OZseq @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1373]) ).

thf(1165,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Limits_Otendsto @ B @ C @ D @ E @ A )
      | ~ ( c_Limits_OZfun @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ E ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ E @ A @ A ) @ C ) @ D @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__Zfun__iff_1) ).

thf(4052,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Limits_Otendsto @ B @ C @ D @ E @ A )
      | ~ ( c_Limits_OZfun @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ E ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ E @ A @ A ) @ C ) @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1165]) ).

thf(665,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).

thf(2899,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(1289,axiom,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).

thf(4336,plain,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1289]) ).

thf(525,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_4) ).

thf(2582,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(1076,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).

thf(3849,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1076]) ).

thf(1318,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).

thf(4405,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1318]) ).

thf(721,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__iff_0) ).

thf(3031,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).

thf(110,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(1662,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(1202,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_Power_Opower @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ tc_nat @ A ) @ B ) @ ( c_Power_Opower__class_Opower @ A ) ) @ C ) @ B @ tc_nat @ A ) @ D ) @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ F ) @ D ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__power_0) ).

thf(4136,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ~ ( class_Power_Opower @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ tc_nat @ A ) @ B ) @ ( c_Power_Opower__class_Opower @ A ) ) @ C ) @ B @ tc_nat @ A ) @ D ) @ E @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ F ) @ D ) @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1202]) ).

thf(539,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).

thf(2614,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(309,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

thf(2096,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(1114,axiom,
    ( ( c_HOL_Oord__class_Oless @ v_n @ tc_nat )
    = ( c_lessequals @ ( hAPP @ c_Suc @ v_n ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le__raw_0) ).

thf(3936,plain,
    ( ( c_HOL_Oord__class_Oless @ v_n @ tc_nat )
    = ( c_lessequals @ ( hAPP @ c_Suc @ v_n ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1114]) ).

thf(314,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

thf(2107,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(1398,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).

thf(4580,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1398]) ).

thf(706,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0_0) ).

thf(2994,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(838,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).

thf(3293,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[838]) ).

thf(1406,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ B )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I28_J_0) ).

thf(4598,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ B )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1406]) ).

thf(1003,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__Suc__diff__eq2_0) ).

thf(3672,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1003]) ).

thf(221,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_3) ).

thf(1905,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(3,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(1420,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(490,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).

thf(2503,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(120,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(1684,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(545,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_Otendsto @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ D @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ F ) @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ D @ F @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ E @ G @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Otendsto_0) ).

thf(2629,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_Otendsto @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ C ) @ D @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ F ) @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ D @ F @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ E @ G @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(677,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ D ) ) @ B ) ) @ C ) @ tc_nat ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff1_1) ).

thf(2927,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ C ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ D ) @ B ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ D ) ) @ B ) ) @ C ) @ tc_nat ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(1132,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).

thf(3975,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
      | ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1132]) ).

thf(728,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__mult__iff_1) ).

thf(3048,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).

thf(1391,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

thf(4566,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1391]) ).

thf(570,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).

thf(2684,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).

thf(355,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).

thf(2202,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(908,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).

thf(3455,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[908]) ).

thf(27,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) )
      | ( ( hAPP @ c_Suc @ A )
        = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).

thf(1472,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) )
      | ( ( hAPP @ c_Suc @ A )
        = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(415,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).

thf(2333,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(517,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(2564,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(831,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).

thf(3278,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[831]) ).

thf(1399,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(4581,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1399]) ).

thf(1162,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_0) ).

thf(4045,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1162]) ).

thf(881,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).

thf(3391,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[881]) ).

thf(584,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).

thf(2715,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).

thf(247,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).

thf(1961,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(1299,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).

thf(4360,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1299]) ).

thf(699,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ( C = E )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).

thf(2977,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ( C = E )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(804,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).

thf(3214,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[804]) ).

thf(103,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).

thf(1647,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(1375,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).

thf(4534,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1375]) ).

thf(766,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_0) ).

thf(3129,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).

thf(1531,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(975,axiom,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).

thf(3608,plain,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[975]) ).

thf(572,axiom,
    ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).

thf(2689,plain,
    ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(494,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__divide_0) ).

thf(2513,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(518,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).

thf(2567,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_3) ).

thf(1547,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(148,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_7) ).

thf(1748,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(989,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).

thf(3640,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).

thf(849,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__vector @ B )
      | ( c_Lim_OLIM @ C @ D @ E @ B @ A )
      | ~ ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ A @ B ) @ C ) @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ B ) @ D ) ) @ ( c_HOL_Ozero__class_Ozero @ B ) @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__offset__zero__cancel_0) ).

thf(3315,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__vector @ B )
      | ( c_Lim_OLIM @ C @ D @ E @ B @ A )
      | ~ ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ A @ B ) @ C ) @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ B ) @ D ) ) @ ( c_HOL_Ozero__class_Ozero @ B ) @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(1073,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).

thf(3842,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1073]) ).

thf(1356,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__div__algebra @ B )
      | ( c_Lim_OisCont @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B ) ) @ C ) @ D @ A @ B )
      | ( ( hAPP @ C @ D )
        = ( c_HOL_Ozero__class_Ozero @ B ) )
      | ~ ( c_Lim_OisCont @ C @ D @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__inverse_0) ).

thf(4490,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__div__algebra @ B )
      | ( c_Lim_OisCont @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B ) ) @ C ) @ D @ A @ B )
      | ( ( hAPP @ C @ D )
        = ( c_HOL_Ozero__class_Ozero @ B ) )
      | ~ ( c_Lim_OisCont @ C @ D @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1356]) ).

thf(292,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_6) ).

thf(2060,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(1257,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ A ) @ B ) @ C ) @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ C @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ B @ ( hAPP @ C @ D ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__compose_0) ).

thf(4272,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ A ) @ B ) @ C ) @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ C @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ B @ ( hAPP @ C @ D ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1257]) ).

thf(329,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).

thf(2143,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(270,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(2012,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).

thf(1605,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(528,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__imp__le_0) ).

thf(2588,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(592,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ C )
        = ( c_Series_Osuminf @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A ) )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_suminf__mult2_0) ).

thf(2732,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ C )
        = ( c_Series_Osuminf @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A ) )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(911,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).

thf(3462,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ B @ D ) )
      | ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[911]) ).

thf(566,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D ) ) @ E ) @ A ) @ F ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).

thf(2678,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D ) ) @ E ) @ A ) @ F ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ E ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(496,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

thf(2518,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(1368,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__vector @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ A @ B ) @ C ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ B ) @ B @ B @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B ) @ E ) @ D ) @ F @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__offset_0) ).

thf(4517,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__vector @ B )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ A @ B ) @ C ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ B ) @ B @ B @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B ) @ E ) @ D ) @ F @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1368]) ).

thf(810,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_Otendsto @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) @ F @ B @ A )
      | ~ ( c_Limits_Otendsto @ D @ E @ F @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Otendsto_0) ).

thf(3228,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Limits_Otendsto @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ B ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) @ F @ B @ A )
      | ~ ( c_Limits_Otendsto @ D @ E @ F @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(1346,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__nat_Odiff__0_0) ).

thf(4469,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1346]) ).

thf(802,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left__number__of_1) ).

thf(3209,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[802]) ).

thf(586,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).

thf(2720,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( B
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(1086,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).

thf(3872,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Ovimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1086]) ).

thf(1307,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(4377,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1307]) ).

thf(577,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ B )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).

thf(2700,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ B )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(1383,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_2) ).

thf(4549,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1383]) ).

thf(1237,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Limits_OZfun @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ D @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ C @ E @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zfun__diff_0) ).

thf(4222,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Limits_OZfun @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ D @ E @ B @ A )
      | ~ ( c_Limits_OZfun @ C @ E @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1237]) ).

thf(457,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(2429,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(417,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I2_J_0) ).

thf(2337,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(108,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__imp__of__nat_0) ).

thf(1658,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(1194,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_plus__nat_Oadd__0_0) ).

thf(4117,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1194]) ).

thf(1043,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_2) ).

thf(3769,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1043]) ).

thf(475,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(2468,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(132,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_9) ).

thf(1711,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(716,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ F ) @ G ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ G @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__add_0) ).

thf(3019,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ F ) @ G ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ G @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).

thf(598,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_1) ).

thf(2747,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(519,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_3) ).

thf(2569,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(1333,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OLIMSEQ_0) ).

thf(4437,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1333]) ).

thf(905,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__le__cancel1_0) ).

thf(3448,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[905]) ).

thf(1370,axiom,
    class_Ring__and__Field_Osemiring__0 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).

thf(4522,plain,
    class_Ring__and__Field_Osemiring__0 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1370]) ).

thf(990,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).

thf(3642,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[990]) ).

thf(1293,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OZseq @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A )
      | ~ ( c_SEQ_OZseq @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zseq__mult__right_0) ).

thf(4346,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OZseq @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A )
      | ~ ( c_SEQ_OZseq @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1293]) ).

thf(307,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).

thf(2092,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(1183,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).

thf(4092,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1183]) ).

thf(168,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).

thf(1790,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(259,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).

thf(1987,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(1116,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ A )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse_0) ).

thf(3940,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ A )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1116]) ).

thf(365,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__le__iff_0) ).

thf(2224,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(9,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

thf(1432,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(1064,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__left_0) ).

thf(3818,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1064]) ).

thf(178,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).

thf(1813,plain,
    ! [B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(1011,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_1) ).

thf(3691,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1011]) ).

thf(758,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osums @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__split__initial__segment_0) ).

thf(3114,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osums @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(857,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq_2) ).

thf(3334,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(734,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ C ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ D ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__right__distrib_0) ).

thf(3063,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ C ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ D ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(674,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).

thf(2920,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(389,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).

thf(2276,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(1056,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OZseq @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_SEQ_OZseq @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_OZseq_0) ).

thf(3801,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OZseq @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_SEQ_OZseq @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1056]) ).

thf(1045,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__algebra @ B )
      | ~ ( class_Power_Opower @ B )
      | ( c_Lim_OisCont @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ tc_nat @ B ) @ A ) @ ( c_Power_Opower__class_Opower @ B ) ) @ C ) @ A @ tc_nat @ B ) @ D ) @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ C @ E @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_isCont__power_0) ).

thf(3774,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Oreal__normed__algebra @ B )
      | ~ ( class_Power_Opower @ B )
      | ( c_Lim_OisCont @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ B @ ( tc_fun @ tc_nat @ B ) @ A ) @ ( c_Power_Opower__class_Opower @ B ) ) @ C ) @ A @ tc_nat @ B ) @ D ) @ E @ A @ B )
      | ~ ( c_Lim_OisCont @ C @ E @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1045]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I1_J_0) ).

thf(1763,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(219,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).

thf(1901,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(946,axiom,
    class_Ring__and__Field_Omult__mono1 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).

thf(3544,plain,
    class_Ring__and__Field_Omult__mono1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[946]) ).

thf(57,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( B
        = ( c_Series_Osuminf @ C @ A ) )
      | ~ ( c_Series_Osums @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__unique_0) ).

thf(1538,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( B
        = ( c_Series_Osuminf @ C @ A ) )
      | ~ ( c_Series_Osums @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(1245,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_Finite__Set_Osetprod @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setprod__empty_0) ).

thf(4241,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_Finite__Set_Osetprod @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1245]) ).

thf(508,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).

thf(2545,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(533,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_6) ).

thf(2599,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(118,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_5) ).

thf(1679,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(890,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

thf(3412,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(957,axiom,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).

thf(3564,plain,
    ! [A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[957]) ).

thf(868,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ F ) @ G ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ G @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__diff_0) ).

thf(3359,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ C ) @ D @ B @ A @ A ) @ E @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ F ) @ G ) @ B @ A )
      | ~ ( c_Lim_OLIM @ D @ E @ G @ B @ A )
      | ~ ( c_Lim_OLIM @ C @ E @ F @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(285,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).

thf(2044,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(725,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OCauchy @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A )
      | ~ ( c_SEQ_OCauchy @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_OCauchy_0) ).

thf(3041,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_SEQ_OCauchy @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A )
      | ~ ( c_SEQ_OCauchy @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).

thf(750,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Suc @ A )
       != ( hAPP @ c_Suc @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).

thf(3095,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Suc @ A )
       != ( hAPP @ c_Suc @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(1212,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

thf(4164,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1212]) ).

thf(1021,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).

thf(3715,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(425,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).

thf(2354,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(235,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_0) ).

thf(1934,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(922,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A ) ) @ C ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__eq__add__iff1_1) ).

thf(3488,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A ) ) @ C ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).

thf(1543,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(1167,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(4057,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1167]) ).

thf(436,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).

thf(2379,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(1207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ ( c_Series_Osuminf @ C @ A ) )
        = ( c_Series_Osuminf @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A ) )
      | ~ ( c_Series_Osummable @ C @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_suminf__diff_0) ).

thf(4150,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ ( c_Series_Osuminf @ C @ A ) )
        = ( c_Series_Osuminf @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A ) )
      | ~ ( c_Series_Osummable @ C @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1207]) ).

thf(526,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

thf(2584,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(565,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).

thf(2675,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(376,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).

thf(2247,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(514,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__inverse__le__neg_0) ).

thf(2558,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(317,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OatMost @ B @ A )
       != ( c_SetInterval_Oord__class_OatMost @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__eq__iff_0) ).

thf(2113,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_SetInterval_Oord__class_OatMost @ B @ A )
       != ( c_SetInterval_Oord__class_OatMost @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(1201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
       != ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) )
      | ( B = C )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).

thf(4133,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
       != ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) )
      | ( B = C )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1201]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).

thf(1536,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(256,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

thf(1981,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(173,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).

thf(1802,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(924,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).

thf(3493,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).

thf(507,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).

thf(2543,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(1247,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

thf(4246,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1247]) ).

thf(867,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).

thf(3356,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(1355,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).

thf(4488,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1355]) ).

thf(698,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__mono_0) ).

thf(2975,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(1365,axiom,
    class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).

thf(4510,plain,
    class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1365]) ).

thf(244,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

thf(1955,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(330,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_0) ).

thf(2145,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

thf(1485,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(1189,axiom,
    ( ( c_SetInterval_Oord__class_OatMost @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
    = ( c_Set_Oinsert @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__0_0) ).

thf(4106,plain,
    ( ( c_SetInterval_Oord__class_OatMost @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
    = ( c_Set_Oinsert @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1189]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).

thf(1506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(880,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ tc_Complex_Ocomplex ) @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ) @ ( c_FFT__Mirabelle_Oroot @ A ) ) ) @ B ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__summation__inv_0) ).

thf(3388,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ tc_Complex_Ocomplex ) @ ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ) @ ( c_FFT__Mirabelle_Oroot @ A ) ) ) @ B ) ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[880]) ).

thf(42,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).

thf(1504,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(1243,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

thf(4235,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1243]) ).

thf(76,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_4) ).

thf(1585,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(493,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_4) ).

thf(2511,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(171,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(1797,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(718,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).

thf(3024,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(760,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ A ) @ B ) @ C ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ F ) @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A )
      | ~ ( c_Deriv_Oderiv @ B @ ( hAPP @ C @ D ) @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__chain2_0) ).

thf(3117,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ A ) @ B ) @ C ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ F ) @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A )
      | ~ ( c_Deriv_Oderiv @ B @ ( hAPP @ C @ D ) @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(687,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).

thf(2949,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(590,axiom,
    class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

thf(2728,plain,
    class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(1118,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0__less__iff_1) ).

thf(3943,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1118]) ).

thf(1125,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ B ) ) @ C ) ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).

thf(3961,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ B ) ) @ C ) ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1125]) ).

thf(738,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__self_0) ).

thf(3071,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(822,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

thf(3256,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(662,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osummable @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A )
      | ~ ( c_Series_Osummable @ C @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__add_0) ).

thf(2892,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osummable @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A )
      | ~ ( c_Series_Osummable @ C @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(209,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

thf(1881,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(1104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__mono1_0) ).

thf(3914,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1104]) ).

thf(936,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ( C = E )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).

thf(3520,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ( C = E )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(871,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).

thf(3366,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[871]) ).

thf(1008,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__diff__iff_1) ).

thf(3684,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).

thf(1313,axiom,
    ! [A: $i] :
      ( ( hAPP @ c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).

thf(4392,plain,
    ! [A: $i] :
      ( ( hAPP @ c_Suc @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1313]) ).

thf(836,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__commute_0) ).

thf(3288,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[836]) ).

thf(1235,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) @ D @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__ignore__initial__segment_0) ).

thf(4217,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) @ D @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1235]) ).

thf(90,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_2) ).

thf(1617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(981,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).

thf(3620,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(471,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).

thf(2458,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ( A = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(64,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_4) ).

thf(1553,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(180,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).

thf(1817,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(983,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_Series_Osuminf @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Series_Osuminf @ C @ A ) ) )
      | ~ ( c_Series_Osummable @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_suminf__mult_0) ).

thf(3625,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_Series_Osuminf @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Series_Osuminf @ C @ A ) ) )
      | ~ ( c_Series_Osummable @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[983]) ).

thf(72,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).

thf(1575,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(298,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

thf(2071,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(1170,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( hAPP @ c_Suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).

thf(4061,plain,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( hAPP @ c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1170]) ).

thf(724,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ B @ C @ A )
      | ~ ( c_SEQ_OZseq @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__Zseq__iff_1) ).

thf(3039,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ B @ C @ A )
      | ~ ( c_SEQ_OZseq @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(651,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Odiff__right_0) ).

thf(2865,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(655,axiom,
    class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).

thf(2875,plain,
    class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).

thf(238,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).

thf(1940,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(227,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).

thf(1918,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(1203,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

thf(4138,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1203]) ).

thf(909,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ ( hAPP @ c_Suc @ C ) ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) ) @ tc_nat @ A @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ c_Suc @ C ) @ tc_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__realpow__diff__sumr2_0) ).

thf(3457,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__ring @ A )
      | ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ ( hAPP @ c_Suc @ C ) ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) ) @ tc_nat @ A @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( hAPP @ c_Suc @ C ) @ tc_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(424,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).

thf(2352,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(1038,axiom,
    ! [A: $i] :
      ( ( A
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__lt__two__imp__zero__or__one_0) ).

thf(3757,plain,
    ! [A: $i] :
      ( ( A
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1038]) ).

thf(480,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( c_SEQ_OCauchy @ B @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__imp__Cauchy_0) ).

thf(2479,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ( c_SEQ_OCauchy @ B @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(1409,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).

thf(4606,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1409]) ).

thf(958,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( B
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__is__add_3) ).

thf(3565,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( B
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).

thf(305,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

thf(2088,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(967,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).

thf(3589,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ C ) ) @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ E ) @ B ) ) @ C ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(1283,axiom,
    class_Lattices_Oupper__semilattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).

thf(4325,plain,
    class_Lattices_Oupper__semilattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1283]) ).

thf(629,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).

thf(2818,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
      = ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(736,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B ) ) @ ( hAPP @ c_Suc @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__diff__diff_0) ).

thf(3067,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ c_Suc @ A ) ) @ B ) ) @ ( hAPP @ c_Suc @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(225,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).

thf(1913,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(301,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).

thf(2078,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(1325,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).

thf(4419,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1325]) ).

thf(193,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).

thf(1844,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(1087,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).

thf(3874,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
     != ( c_Set_Oinsert @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1087]) ).

thf(422,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

thf(2347,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(106,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__less__iff_0) ).

thf(1654,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) @ A ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(538,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A ) )
        = B )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__inverse_0) ).

thf(2611,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A ) )
        = B )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(411,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).

thf(2325,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(1221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).

thf(4185,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1221]) ).

thf(596,axiom,
    ! [A: $i] :
      ( ( c_SetInterval_Oord__class_OatMost @ ( hAPP @ c_Suc @ A ) @ tc_nat )
      = ( c_Set_Oinsert @ ( hAPP @ c_Suc @ A ) @ ( c_SetInterval_Oord__class_OatMost @ A @ tc_nat ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__Suc_0) ).

thf(2743,plain,
    ! [A: $i] :
      ( ( c_SetInterval_Oord__class_OatMost @ ( hAPP @ c_Suc @ A ) @ tc_nat )
      = ( c_Set_Oinsert @ ( hAPP @ c_Suc @ A ) @ ( c_SetInterval_Oord__class_OatMost @ A @ tc_nat ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).

thf(707,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_1) ).

thf(2997,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(485,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

thf(2490,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(1187,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ C @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__sum_0) ).

thf(4102,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ C @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1187]) ).

thf(862,axiom,
    class_Ring__and__Field_Omult__mono @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).

thf(3346,plain,
    class_Ring__and__Field_Omult__mono @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(1146,axiom,
    hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_1) ).

thf(4006,plain,
    hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1146]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).

thf(2226,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
        = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(18,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( hAPP @ c_Suc @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).

thf(1453,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( hAPP @ c_Suc @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(552,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).

thf(2643,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(1394,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osums @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Osums_0) ).

thf(4574,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_Series_Osums @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A )
      | ~ ( c_Series_Osums @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1394]) ).

thf(969,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel1_1) ).

thf(3593,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(920,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).

thf(3484,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ A @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(44,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).

thf(1508,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(1380,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

thf(4542,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1380]) ).

thf(696,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ B ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_division__ring__inverse__diff_0) ).

thf(2971,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ B ) ) ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).

thf(710,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).

thf(3003,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(872,axiom,
    ! [B: $i,A: $i] :
      ( ( c_FFT__Mirabelle_ODFT @ A @ B @ v_i )
      = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ A ) ) ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ v_i ) ) ) @ B @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DFT__def_0) ).

thf(3368,plain,
    ! [B: $i,A: $i] :
      ( ( c_FFT__Mirabelle_ODFT @ A @ B @ v_i )
      = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ tc_Complex_Ocomplex ) ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ A ) ) ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ v_i ) ) ) @ B @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(499,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0) ).

thf(2526,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) )
        = ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(1027,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).

thf(3729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1027]) ).

thf(1103,axiom,
    ! [A: $i] :
      ( ( c_FFT__Mirabelle_Oroot @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__nonzero_0) ).

thf(3911,plain,
    ! [A: $i] :
      ( ( c_FFT__Mirabelle_Oroot @ A )
     != ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1103]) ).

thf(977,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mult__distrib_0) ).

thf(3613,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[977]) ).

thf(580,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ A )
      | ( ( c_Series_Osuminf @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ tc_nat @ A @ A ) @ A )
        = ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_powser__zero_0) ).

thf(2707,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ A )
      | ( ( c_Series_Osuminf @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ tc_nat @ A @ A ) @ A )
        = ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(704,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ B ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__cancel_0) ).

thf(2988,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ B ) ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(531,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).

thf(2594,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(343,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_9) ).

thf(2174,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(392,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).

thf(2283,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(440,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(2389,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(646,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ( C = B )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__cases_0) ).

thf(2853,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ( C = B )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(395,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).

thf(2290,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(378,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(2251,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__leE_0) ).

thf(1903,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(326,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).

thf(2135,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(447,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_0) ).

thf(2406,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(1182,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ B @ tc_nat ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat ) @ ( tc_fun @ tc_nat @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__add__Un_0) ).

thf(4089,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ B @ tc_nat ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) @ tc_nat ) @ ( tc_fun @ tc_nat @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1182]) ).

thf(512,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).

thf(2554,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(31,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_6) ).

thf(1481,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(878,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osums @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ A )
      | ~ ( c_Series_Osums @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ c_Suc ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sums__Suc_0) ).

thf(3383,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osums @ B @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) @ A )
      | ~ ( c_Series_Osums @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ c_Suc ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).

thf(1629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(267,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).

thf(2004,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(1139,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__less__mono_0) ).

thf(3991,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1139]) ).

thf(1034,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ E ) @ F ) @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__add_0) ).

thf(3748,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ E ) @ F ) @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(985,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__0__left_1) ).

thf(3630,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__0 @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).

thf(197,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__mono1_0) ).

thf(1854,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(1290,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).

thf(4338,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1290]) ).

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

thf(3561,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[955]) ).

thf(814,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).

thf(3235,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(458,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_0) ).

thf(2431,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(1148,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ B @ C @ A )
      | ~ ( c_SEQ_OLIMSEQ @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ D @ tc_nat @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__diff__approach__zero_0) ).

thf(4010,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ B @ C @ A )
      | ~ ( c_SEQ_OLIMSEQ @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ D @ tc_nat @ A @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1148]) ).

thf(1358,axiom,
    ! [A: $i] :
      ( ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).

thf(4495,plain,
    ! [A: $i] :
      ( ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1358]) ).

thf(324,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_7) ).

thf(2130,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(1080,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).

thf(3859,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1080]) ).

thf(333,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(2152,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(383,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(2262,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(1339,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__diff__rev__if_0) ).

thf(4451,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ tc_nat ) @ C ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1339]) ).

thf(1253,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Oone__class_Oone @ A ) )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__unique_0) ).

thf(4261,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C )
       != ( c_HOL_Oone__class_Oone @ A ) )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1253]) ).

thf(746,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ B )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__inverse_0) ).

thf(3085,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ B )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(269,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_1) ).

thf(2009,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(1133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).

thf(3978,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1133]) ).

thf(1226,axiom,
    hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ v_i @ tc_nat ) @ v_n ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_0) ).

thf(4197,plain,
    hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ v_i @ tc_nat ) @ v_n ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1226]) ).

thf(1096,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).

thf(3896,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1096]) ).

thf(522,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).

thf(2576,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(1005,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).

thf(3677,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(86,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

thf(1607,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(667,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).

thf(2902,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(406,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).

thf(2315,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).

thf(1444,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(1275,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).

thf(4306,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1275]) ).

thf(789,axiom,
    class_Int_Onumber @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).

thf(3181,plain,
    class_Int_Onumber @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(438,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D )
        = C )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_0) ).

thf(2384,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D )
        = C )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(615,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBS__def_0) ).

thf(2786,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( c_COMBS @ A @ B @ C @ D @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ ( hAPP @ B @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(620,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).

thf(2796,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(1268,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).

thf(4293,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1268]) ).

thf(1217,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).

thf(4175,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Obounded__lattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != ( c_Orderings_Obot__class_Obot @ A ) )
      | ( C
        = ( c_Orderings_Obot__class_Obot @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1217]) ).

thf(926,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( hAPP @ c_Suc @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).

thf(3497,plain,
    ! [A: $i] :
      ( ( c_HOL_Ozero__class_Ozero @ tc_nat )
     != ( hAPP @ c_Suc @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).

thf(1208,axiom,
    ! [A: $i] :
      ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( hAPP @ c_Suc @ A ) @ tc_nat )
      = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__singleton_0) ).

thf(4153,plain,
    ! [A: $i] :
      ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( hAPP @ c_Suc @ A ) @ tc_nat )
      = ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1208]) ).

thf(1089,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ( B = D )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_0) ).

thf(3879,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ( B = D )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1089]) ).

thf(1233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__assoc_0) ).

thf(4214,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ C )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1233]) ).

thf(1074,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__mono2_0) ).

thf(3844,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1074]) ).

thf(162,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).

thf(1777,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(1271,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).

thf(4299,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1271]) ).

thf(971,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__add__left__cancel_0) ).

thf(3598,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(12,axiom,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__Suc1_0) ).

thf(1440,plain,
    ! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ ( hAPP @ c_Suc @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(775,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).

thf(3149,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[775]) ).

thf(940,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A ) )
        = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff__inverse_0) ).

thf(3529,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A ) )
        = B )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(130,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less_0) ).

thf(1706,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ E @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(1053,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F )
      = ( hAPP @ D @ ( hAPP @ E @ F ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBB__def_0) ).

thf(3793,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F )
      = ( hAPP @ D @ ( hAPP @ E @ F ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1053]) ).

thf(567,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).

thf(2680,plain,
    class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(347,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__inverse__le_0) ).

thf(2183,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(865,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diffs0__imp__equal_0) ).

thf(3351,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(1140,axiom,
    class_Ring__and__Field_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).

thf(3993,plain,
    class_Ring__and__Field_Ocomm__semiring__0 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1140]) ).

thf(1176,axiom,
    class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).

thf(4074,plain,
    class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1176]) ).

thf(1337,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ E ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).

thf(4446,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ D ) @ E ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ E ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1337]) ).

thf(215,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

thf(1893,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(281,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).

thf(2036,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(991,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Onoteq__reduce_1) ).

thf(3645,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[991]) ).

thf(673,axiom,
    ! [A: $i] :
      ( ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).

thf(2917,plain,
    ! [A: $i] :
      ( ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(1305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ C )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

thf(4372,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C ) ) @ C )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1305]) ).

thf(1040,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
      | ( D = E )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).

thf(3761,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
      | ( D = E )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1040]) ).

thf(612,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ B )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__inverse2_0) ).

thf(2779,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ B )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).

thf(273,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).

thf(2019,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(893,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_SEQ_OCauchy @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_SEQ_OCauchy @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_OCauchy_0) ).

thf(3420,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_SEQ_OCauchy @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_SEQ_OCauchy @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(89,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero_0) ).

thf(1614,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(434,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

thf(2374,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(394,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ c_Suc @ B ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__Suc_0) ).

thf(2287,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( hAPP @ c_Suc @ B ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(101,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

thf(1642,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(1512,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(569,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(2683,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).

thf(1050,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).

thf(3785,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1050]) ).

thf(1250,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).

thf(4254,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1250]) ).

thf(825,axiom,
    class_Lattices_Olattice @ tc_bool,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).

thf(3264,plain,
    class_Lattices_Olattice @ tc_bool,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[825]) ).

thf(1371,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ ( hAPP @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ F ) @ ( hAPP @ B @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ c_Suc @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ) @ A )
      | ( ( hAPP @ C @ D )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__quotient_0) ).

thf(4523,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ ( hAPP @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ F ) @ ( hAPP @ B @ D ) ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ C @ D ) ) @ ( hAPP @ c_Suc @ ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ) ) @ A )
      | ( ( hAPP @ C @ D )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1371]) ).

thf(628,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).

thf(2815,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(1302,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osummable @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A )
      | ~ ( c_Series_Osummable @ C @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__diff_0) ).

thf(4367,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_Series_Osummable @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ tc_nat @ A @ A ) @ A )
      | ~ ( c_Series_Osummable @ C @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1302]) ).

thf(799,axiom,
    class_RealVector_Ometric__space @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Ometric__space) ).

thf(3203,plain,
    class_RealVector_Ometric__space @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(781,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_SEQ_OZseq @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_SEQ_OZseq @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_OZseq_0) ).

thf(3164,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_SEQ_OZseq @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ A )
      | ~ ( c_SEQ_OZseq @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(997,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

thf(3658,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(321,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_3) ).

thf(2123,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(73,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_9) ).

thf(1578,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(245,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).

thf(1957,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(1316,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).

thf(4399,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1316]) ).

thf(334,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).

thf(2155,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(380,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).

thf(2255,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(1297,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ C @ D @ ( hAPP @ C @ D ) @ A @ B )
      | ~ ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ A ) @ C ) @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ C @ D ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__isCont__iff_1) ).

thf(4356,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ( c_Lim_OLIM @ C @ D @ ( hAPP @ C @ D ) @ A @ B )
      | ~ ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ A ) @ C ) @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ D ) ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( hAPP @ C @ D ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1297]) ).

thf(1142,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ E ) @ C ) ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ E ) ) ) @ C ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divides__special_0) ).

thf(3997,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ E ) @ C ) ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ E ) ) ) @ C ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1142]) ).

thf(1101,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(3907,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1101]) ).

thf(972,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__le__mono_0) ).

thf(3601,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ C ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(369,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).

thf(2233,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(1090,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

thf(3882,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1090]) ).

thf(1137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OgreaterThanLessThan @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThanLessThan__empty_0) ).

thf(3987,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_SetInterval_Oord__class_OgreaterThanLessThan @ B @ C @ A )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1137]) ).

thf(1071,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBC__def_0) ).

thf(3837,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
      = ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1071]) ).

thf(912,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_0) ).

thf(3464,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[912]) ).

thf(535,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).

thf(2604,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(1052,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ B )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__inverse_0) ).

thf(3790,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) @ B )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1052]) ).

thf(858,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_1) ).

thf(3337,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).

thf(1673,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(152,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).

thf(1757,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(925,axiom,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

thf(3496,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(1397,axiom,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

thf(4579,plain,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1397]) ).

thf(607,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ E ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).

thf(2768,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ E ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(260,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).

thf(1989,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(1295,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).

thf(4350,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1295]) ).

thf(1349,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__diff_0) ).

thf(4474,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1349]) ).

thf(1147,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I9_J_0) ).

thf(4007,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1147]) ).

thf(692,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel1_0) ).

thf(2961,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).

thf(1158,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).

thf(4034,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ D )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1158]) ).

thf(986,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Series_Osuminf @ C @ A ) )
        = ( c_Series_Osuminf @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A ) )
      | ~ ( c_Series_Osummable @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Osuminf_0) ).

thf(3633,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Series_Osuminf @ C @ A ) )
        = ( c_Series_Osuminf @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ A ) )
      | ~ ( c_Series_Osummable @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[986]) ).

thf(541,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_3) ).

thf(2619,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(2040,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(562,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I3_J_0) ).

thf(2668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(846,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__cancel_0) ).

thf(3309,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) )
      = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(1135,axiom,
    ! [B: $i,A: $i] :
      ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).

thf(3982,plain,
    ! [B: $i,A: $i] :
      ( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
      | ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1135]) ).

thf(600,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__diff__right_0) ).

thf(2751,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(1123,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ~ ( class_RealVector_Ometric__space @ C )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F @ ( hAPP @ D @ G ) @ C @ B )
      | ~ ( c_Lim_OLIM @ E @ F @ G @ C @ A )
      | ~ ( c_Lim_OLIM @ D @ G @ ( hAPP @ D @ G ) @ A @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIM__compose_0) ).

thf(3956,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Ometric__space @ A )
      | ~ ( class_RealVector_Ometric__space @ B )
      | ~ ( class_RealVector_Ometric__space @ C )
      | ( c_Lim_OLIM @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ B @ C ) @ D ) @ E ) @ F @ ( hAPP @ D @ G ) @ C @ B )
      | ~ ( c_Lim_OLIM @ E @ F @ G @ C @ A )
      | ~ ( c_Lim_OLIM @ D @ G @ ( hAPP @ D @ G ) @ A @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1123]) ).

thf(1156,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ C @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__mult_0) ).

thf(4029,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ C @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1156]) ).

thf(1218,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__0_1) ).

thf(4178,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1218]) ).

thf(1261,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).

thf(4281,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ C ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1261]) ).

thf(863,axiom,
    class_Int_Onumber__ring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

thf(3347,plain,
    class_Int_Onumber__ring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[863]) ).

thf(125,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_1) ).

thf(1693,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(1180,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).

thf(4083,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
      | ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1180]) ).

thf(1154,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__is__1_2) ).

thf(4024,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B )
       != ( hAPP @ c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1154]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) ) @ C )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_4) ).

thf(1561,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) ) @ C )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(579,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).

thf(2704,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(671,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__0__less__mult__iff_2) ).

thf(2913,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(446,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

thf(2404,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(583,axiom,
    class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).

thf(2714,plain,
    class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).

thf(796,axiom,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).

thf(3196,plain,
    ! [B: $i,A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(214,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

thf(1891,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(727,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).

thf(3045,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Odistrib__lattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(930,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).

thf(3506,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
        = ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(274,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_1) ).

thf(2021,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(294,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_0) ).

thf(2063,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(1280,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) @ E ) ) @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) @ F ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).

thf(4318,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ C ) @ D ) ) @ E ) ) @ F ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) @ F ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1280]) ).

thf(510,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_3) ).

thf(2549,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( B
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(233,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_0) ).

thf(1930,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(818,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).

thf(3244,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ B ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(1131,axiom,
    class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

thf(3974,plain,
    class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1131]) ).

thf(694,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) @ D ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ D ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__add__iff2_0) ).

thf(2966,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ B ) @ C ) ) @ D ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) ) @ A ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ B ) @ D ) ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(75,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).

thf(1582,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Olower__semilattice @ A )
      | ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(1353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) @ B ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__diff__split_1) ).

thf(4484,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ C ) ) @ B ) ) )
      | ( hBOOL @ ( hAPP @ A @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1353]) ).

thf(1314,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(4395,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1314]) ).

thf(1152,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__assoc2_0) ).

thf(4019,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ A ) @ B ) ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ C ) ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1152]) ).

thf(742,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

thf(3076,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ B ) @ C )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(1361,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).

thf(4501,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ E ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1361]) ).

thf(373,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).

thf(2241,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(323,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__fieldgb_Odivide__inverse_0) ).

thf(2127,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(336,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).

thf(2159,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ c_Suc @ A ) @ tc_nat ) @ ( hAPP @ c_Suc @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(626,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).

thf(2810,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ E ) ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(1199,axiom,
    class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

thf(4129,plain,
    class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1199]) ).

thf(186,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).

thf(1829,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(254,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).

thf(1977,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(732,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( c_Series_Osummable @ B @ A )
      | ( ( c_Series_Osuminf @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_suminf__minus__initial__segment_0) ).

thf(3057,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( c_Series_Osummable @ B @ A )
      | ( ( c_Series_Osuminf @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ A @ tc_nat ) @ B ) @ ( hAPP @ ( c_COMBC @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ tc_nat @ tc_nat @ tc_nat ) @ C ) ) @ A )
        = ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A ) @ ( c_Series_Osuminf @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_nat ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).

thf(623,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

thf(2803,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(643,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__strict__increasing__iff_0) ).

thf(2847,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(960,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero_0) ).

thf(3570,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(483,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).

thf(2485,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(1044,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).

thf(3772,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1044]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one__over_0) ).

thf(1550,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ C ) )
        = ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(1363,axiom,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).

thf(4506,plain,
    ! [A: $i] :
      ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1363]) ).

thf(823,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).

thf(3259,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(1172,axiom,
    class_Lattices_Olattice @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).

thf(4066,plain,
    class_Lattices_Olattice @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1172]) ).

thf(40,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_7) ).

thf(1500,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(1127,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Limits_Otendsto @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ D @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ E ) @ F ) @ G @ B @ A )
      | ( F
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Limits_Otendsto @ D @ F @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ E @ G @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tendsto__divide_0) ).

thf(3965,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Limits_Otendsto @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ D @ B @ A @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ E ) @ F ) @ G @ B @ A )
      | ( F
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Limits_Otendsto @ D @ F @ G @ B @ A )
      | ~ ( c_Limits_Otendsto @ C @ E @ G @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1127]) ).

thf(230,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

thf(1923,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(1320,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ A ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__cmult_0) ).

thf(4410,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ A ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) ) @ C ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ E ) @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1320]) ).

thf(1230,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) )
       != ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ ( hAPP @ c_Suc @ C ) ) )
      | ( B = D )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__base_0) ).

thf(4206,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( hAPP @ c_Suc @ C ) )
       != ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ D ) @ ( hAPP @ c_Suc @ C ) ) )
      | ( B = D )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1230]) ).

thf(943,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).

thf(3538,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Olattice @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(231,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).

thf(1925,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(1286,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__eq__0_0) ).

thf(4330,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
      = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1286]) ).

thf(505,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).

thf(2539,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(133,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).

thf(1713,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_6) ).

thf(1597,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ C ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(650,axiom,
    class_Ring__and__Field_Ocomm__semiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

thf(2864,plain,
    class_Ring__and__Field_Ocomm__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(1031,axiom,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__is__0_0) ).

thf(3740,plain,
    ! [B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B )
       != ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1031]) ).

thf(211,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).

thf(1885,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(1061,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(3812,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1061]) ).

thf(1106,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ ( hAPP @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ F ) @ ( hAPP @ B @ D ) ) ) @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__mult_0) ).

thf(3918,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ ( hAPP @ C @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ F ) @ ( hAPP @ B @ D ) ) ) @ A )
      | ~ ( c_Deriv_Oderiv @ C @ D @ F @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1106]) ).

thf(386,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_2) ).

thf(2270,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(1300,axiom,
    ! [A: $i] :
      ( A
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_1) ).

thf(4363,plain,
    ! [A: $i] :
      ( A
      = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1300]) ).

thf(433,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

thf(2372,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(916,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
      | ( B = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).

thf(3474,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ A @ tc_nat ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ A ) )
      | ( B = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(657,axiom,
    ! [B: $i,A: $i] :
      ( ( c_FFT__Mirabelle_OIDFT @ A @ B @ v_i )
      = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ tc_Complex_Ocomplex ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ A ) ) ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ v_i ) ) @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IDFT__def_0) ).

thf(2879,plain,
    ! [B: $i,A: $i] :
      ( ( c_FFT__Mirabelle_OIDFT @ A @ B @ v_i )
      = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ tc_Complex_Ocomplex ) @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_Complex_Ocomplex @ ( tc_fun @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ tc_Complex_Ocomplex ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_COMBB @ tc_nat @ tc_Complex_Ocomplex @ tc_nat ) @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ A ) ) ) @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ v_i ) ) @ tc_nat @ tc_Complex_Ocomplex @ tc_Complex_Ocomplex ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(900,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__diff_0) ).

thf(3437,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_lessequals @ A @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ B ) @ A ) ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(1258,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_OLIMSEQ_0) ).

thf(4274,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ B ) @ tc_nat @ A @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ D ) @ C ) @ A )
      | ~ ( c_SEQ_OLIMSEQ @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1258]) ).

thf(1400,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

thf(4584,plain,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1400]) ).

thf(658,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__eq__inf__sup_0) ).

thf(2881,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).

thf(803,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ C @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__diff_0) ).

thf(3212,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( c_COMBS @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ A ) @ ( c_HOL_Ominus__class_Ominus @ A ) ) @ B ) @ C @ A @ A @ A ) @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ C @ D @ A )
      | ~ ( c_Deriv_Odifferentiable @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(23,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(1463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ C @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(898,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( c_HOL_Oinverse__class_Oinverse @ A ) ) @ B ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) @ A )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_SEQ_OLIMSEQ @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_LIMSEQ__inverse_0) ).

thf(3432,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
      | ( c_SEQ_OLIMSEQ @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ tc_nat ) @ ( c_HOL_Oinverse__class_Oinverse @ A ) ) @ B ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ C ) @ A )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_SEQ_OLIMSEQ @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(469,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_summable__LIMSEQ__zero_0) ).

thf(2453,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_SEQ_OLIMSEQ @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_Series_Osummable @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(951,axiom,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
      = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__cancel1_1) ).

thf(3553,plain,
    ! [B: $i,A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ A )
      = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(1024,axiom,
    ! [B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__r0__iff_0) ).

thf(3721,plain,
    ! [B: $i,A: $i] :
      ( ( A
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1024]) ).

thf(1036,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ C @ D @ tc_nat ) ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__add__nat__ivl__singleton_0) ).

thf(3753,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ C @ D @ tc_nat ) ) )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ tc_nat @ A ) @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ tc_nat ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ tc_nat ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1036]) ).

thf(1098,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__mult__less__cancel1_1) ).

thf(3901,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ tc_nat ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1098]) ).

thf(939,axiom,
    class_Orderings_Opreorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(3528,plain,
    class_Orderings_Opreorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(601,axiom,
    ( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root0_0) ).

thf(2754,plain,
    ( ( c_FFT__Mirabelle_Oroot @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
    = ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(409,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_9) ).

thf(2321,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(240,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).

thf(1944,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oupper__semilattice @ A )
      | ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
       != C )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(1386,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ B @ A @ A ) @ E ) ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Osetsum_0) ).

thf(4555,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ C ) @ D ) ) @ E )
        = ( hAPP @ ( hAPP @ ( c_Finite__Set_Osetsum @ B @ A ) @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ A @ A ) @ B ) @ ( c_HOL_Oinverse__class_Odivide @ A ) ) @ C ) @ B @ A @ A ) @ E ) ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1386]) ).

thf(357,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_5) ).

thf(2206,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(143,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).

thf(1737,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(119,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).

thf(1681,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(887,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff__number__of_0) ).

thf(3405,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ tc_nat ) )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[887]) ).

thf(1211,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power__eq__number__of_2) ).

thf(4161,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat )
        = ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_nat ) ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1211]) ).

thf(636,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).

thf(2832,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).

thf(1382,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).

thf(4547,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1382]) ).

thf(461,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(2436,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(462,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_1) ).

thf(2438,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(35,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_8) ).

thf(1490,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(398,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).

thf(2297,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(1278,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add__join @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__sup__distrib__right_0) ).

thf(4313,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add__join @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D )
        = ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1278]) ).

thf(903,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

thf(3443,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ D ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[903]) ).

thf(158,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

thf(1769,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ B ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(1327,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ tc_nat @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ A ) ) @ B ) @ A @ tc_nat @ A ) @ ( hAPP @ c_Suc @ C ) ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ B @ D ) ) @ C ) ) ) @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__power__Suc_0) ).

thf(4423,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Oderiv @ ( hAPP @ ( c_COMBC @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ ( tc_fun @ tc_nat @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ A ) ) @ B ) @ A @ tc_nat @ A ) @ ( hAPP @ c_Suc @ C ) ) @ D @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ E ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ A ) @ ( hAPP @ B @ D ) ) @ C ) ) ) @ A )
      | ~ ( c_Deriv_Oderiv @ B @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1327]) ).

thf(1223,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

thf(4189,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1223]) ).

thf(341,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).

thf(2170,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ C @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(637,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).

thf(2834,plain,
    ! [B: $i,A: $i] :
      ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
      = B ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(350,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).

thf(2191,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ C ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ D ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(16,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).

thf(1449,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).

thf(1468,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ B ) @ C ) @ A ) @ D ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ C ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(476,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__half__sum_0) ).

thf(2470,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ ( c_HOL_Oone__class_Oone @ A ) ) ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ C ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(700,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).

thf(2980,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( hBOOL @ ( hAPP @ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ D ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_lessequals @ D @ A ) @ C ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(962,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ( B = D )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_natgb_Oadd__mul__solve_0) ).

thf(3575,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ D ) )
       != ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ A ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ tc_nat ) @ C ) @ B ) ) )
      | ( B = D )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(1385,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ A ) ) @ B ) @ C @ A )
      | ( ( hAPP @ B @ C )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Deriv_Odifferentiable @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_differentiable__inverse_0) ).

thf(4552,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( c_Deriv_Odifferentiable @ ( hAPP @ ( hAPP @ ( c_COMBB @ A @ A @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ A ) ) @ B ) @ C @ A )
      | ( ( hAPP @ B @ C )
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_Deriv_Odifferentiable @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1385]) ).

thf(557,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).

thf(2655,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
      = ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(1144,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).

thf(4002,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ D ) @ E ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1144]) ).

thf(2,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__distrib__number__of_0) ).

thf(1417,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ C ) @ D ) )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ A ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_HOL_Otimes__class_Otimes @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) @ D ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(204,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).

thf(1870,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( hAPP @ ( c_HOL_Oinverse__class_Oinverse @ A ) @ B )
        = ( hAPP @ ( hAPP @ ( c_HOL_Oinverse__class_Odivide @ A ) @ ( c_HOL_Oone__class_Oone @ A ) ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(1001,axiom,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__gr__0_2) ).

thf(3669,plain,
    ! [B: $i,A: $i] :
      ( ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ ( hAPP @ ( hAPP @ ( c_HOL_Oplus__class_Oplus @ tc_nat ) @ A ) @ B ) ) )
      | ~ ( hBOOL @ ( hAPP @ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) @ B ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(608,axiom,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ A ) ) @ A )
      = ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_root__unity_0) ).

thf(2771,plain,
    ! [A: $i] :
      ( ( hAPP @ ( hAPP @ ( c_Power_Opower__class_Opower @ tc_Complex_Ocomplex ) @ ( c_FFT__Mirabelle_Oroot @ A ) ) @ A )
      = ( c_HOL_Oone__class_Oone @ tc_Complex_Ocomplex ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(4685,plain,
    $false,
    inference(cvc4,[status(thm)],[2163,3021,2822,4201,2094,4094,1899,2427,4015,3927,2331,3172,1686,4560,1879,1718,2889,1823,2295,2306,3053,3345,4005,4464,2341,3008,2109,2031,3661,1767,3399,1995,3930,4169,3798,1559,3666,4022,2412,2876,4183,4290,3477,3698,1840,3581,3863,3830,1850,2499,1950,1549,1750,2940,4075,2590,3098,2671,1728,2099,4326,4479,2363,4043,3681,3990,4037,2309,3072,2210,3317,4500,2231,2622,4311,2808,3905,1522,3230,2381,3813,2495,2908,2062,3549,2776,1808,2659,3417,3509,3285,3460,1422,2947,1533,4614,3402,1437,4592,2195,1671,3439,2740,1735,3253,2844,1458,1788,1426,2607,2686,3942,3649,3135,4097,4110,1867,1999,3446,2448,2933,2434,2712,3616,4279,3781,4440,3693,4564,2476,2627,2168,4058,3414,1761,3121,3562,1640,2580,2901,3313,4435,2042,3717,2360,3370,4047,1835,4343,2046,3994,1782,3502,3513,3088,4124,2886,1601,2516,2067,4322,2531,1746,3103,3545,2723,4371,1441,4266,1650,1645,4198,3898,3140,1475,1518,1703,3688,2869,4511,4249,1887,4386,2957,3891,4439,3275,2339,4415,4224,3821,1907,3653,2274,3776,3125,2562,2703,4539,4238,3204,3938,3029,4348,3425,1792,1430,2735,1985,4422,3131,1660,4070,3116,3617,2444,1860,4334,2217,4130,3542,3410,2185,3280,3803,2466,4428,3043,3855,2745,2356,2571,3713,4119,3385,4353,1572,3216,1741,4551,3951,1773,1963,3268,1847,1545,2420,1922,2691,3099,1800,4194,4358,2552,1479,1609,2635,2929,3014,4141,4383,2301,1815,4460,1494,4390,4471,3557,1875,2852,3231,3866,2533,4302,4514,2829,3788,4595,2237,3322,3431,1664,2259,2650,2073,2017,2178,2222,2616,4396,3887,2027,4173,3934,4443,4072,1811,4578,2105,2090,3393,4258,3724,1911,4454,3295,3453,2451,1858,4147,3525,1828,2925,1677,2034,3923,3290,3300,3093,4115,2335,2777,3152,2058,2367,4230,2861,2483,1622,2639,3327,2103,3226,4519,3870,2718,3189,2281,3808,2523,1526,2137,4040,3361,3756,4536,1697,3559,4285,3606,4588,3184,2586,2982,2884,1975,1564,2762,3378,3435,2954,4407,1691,2574,2737,2641,3795,3037,3011,4604,3450,3503,4216,3591,3301,2204,3984,3169,3265,3852,4531,1470,1915,1708,3767,4576,2083,4031,4059,2905,2773,1636,2673,3735,2264,1723,3261,4466,2541,1580,4375,2147,3610,3069,4284,2986,3664,2601,3827,2560,3972,2249,3603,1519,2596,4609,1570,1502,4252,3233,4204,3884,4449,4493,2132,3250,3207,2396,2015,3889,3471,3286,1883,3810,1920,3578,2872,3877,4187,3144,1656,2327,3727,1634,3408,2653,2958,3948,3307,3166,3958,4295,3191,2464,1938,3980,1837,4585,2433,3403,1968,3090,3198,4155,2820,3297,3750,1819,1624,2200,2609,4402,3535,2181,3050,2345,2547,2313,4104,3647,4080,3595,4027,4316,1983,3482,2801,1794,1804,1970,1856,3518,4227,2638,4219,3001,3968,2245,1936,3467,1592,3615,1541,2157,2840,4108,4486,1498,1587,2509,3102,3704,2726,2631,3119,3746,3650,4012,3916,1755,3060,3176,3311,3846,3622,2830,2868,4191,1700,3671,3573,2781,1567,4291,4320,2798,3954,4049,4301,2023,1942,4276,2323,3179,4167,1739,1461,4425,1424,3441,2455,4545,2080,1414,2053,1842,2172,4054,3428,3194,2349,2038,1446,1889,3555,4457,1612,2472,2317,1744,3242,3656,1451,2487,3743,2243,1947,3628,1720,2370,3703,1825,2968,2285,3486,2125,2536,3126,2681,2836,1456,4508,3354,2387,1831,1932,4244,3222,2006,2497,4540,3540,1852,2813,3760,3247,1599,2697,1715,3333,3109,1979,3074,4416,3920,2272,2140,4086,2756,3083,3162,3201,1759,3147,1779,2208,4212,1695,3856,2963,1466,1515,1895,2662,4572,3824,2634,2749,3903,1991,2788,3834,4288,2761,3173,4476,3639,2915,2440,2408,2793,2645,3422,3675,4308,2423,2529,2729,2001,2176,2391,1927,4562,4503,3111,1631,2121,2235,3707,1510,2292,4380,1959,2556,2253,2149,3491,1483,3079,4412,4256,3738,4340,3375,1595,3839,3523,4269,3686,4017,2894,4365,3396,2376,3343,3158,3319,2789,2188,1620,3283,1965,2827,4144,3372,4000,3187,3547,1833,3636,2048,3925,2859,2938,4283,1784,4077,2791,3240,2657,2849,2393,1752,1652,3081,3945,3272,4122,2806,2991,2398,4328,4590,3868,4612,2695,1488,2029,4112,4413,3123,3700,1897,2425,3304,2474,1638,1675,3532,1428,3223,2161,4526,4537,4558,1669,2193,1786,4127,2220,3964,3695,4099,3330,4171,1865,2935,1733,3340,1997,2442,2759,3783,2055,3832,2166,1765,3302,3568,3719,2358,2319,4433,3678,2311,2521,2119,3551,1806,3779,3270,4616,4228,2538,4498,4369,3155,2229,3815,3238,2214,3764,2415,2493,1524,3515,3732,2257,1589,1492,1603,2299,4601,3106,3468,2116,2839,1771,2943,3710,2945,2856,3500,3138,3586,1690,3182,3066,2896,2197,3160,2065,4388,1667,4430,1877,2025,3027,4569,2267,2446,4332,3006,4296,3861,2278,3219,2824,3133,3055,2343,2625,4462,2111,3073,4064,1993,1821,1731,4264,3932,1909,1862,4181,3034,2410,2923,3971,3583,1556,1460,2647,2461,2974,2329,2842,1952,3893,2710,2911,2578,1688,3480,2365,4232,2212,1528,2086,3806,2931,3016,3363,1726,4067,2069,2075,2418,2725,2401,2051,2765,2481,1435,1775,2592,1477,3325,3142,2101,4304,1496,2303,3512,3178,2999,3348,3908,2693,4209,2984,1973,4481,4158,2506,4473,3380,1626,2239,2952,1873,2665,2784,4529,4052,2899,4336,2582,3849,4405,3031,1662,4136,2614,2096,3936,2107,4580,2994,3293,4598,3672,1905,1420,2503,1684,2629,2927,3975,3048,4566,2684,2202,3455,1472,2333,2564,3278,4581,4045,3391,2715,1961,4360,2977,3214,1647,4534,3129,1531,3608,2689,2513,2567,1547,1748,3640,3315,3842,4490,2060,4272,2143,2012,1605,2588,2732,3462,2678,2518,4517,3228,4469,3209,2720,3872,4377,2700,4549,4222,2429,2337,1658,4117,3769,2468,1711,3019,2747,2569,4437,3448,4522,3642,4346,2092,4092,1790,1987,3940,2224,1432,3818,1813,3691,3114,3334,3063,2920,2276,3801,3774,1763,1901,3544,1538,4241,2545,2599,1679,3412,3564,3359,2044,3041,3095,4164,3715,2354,1934,3488,1543,4057,2379,4150,2584,2675,2247,2558,2113,4133,1536,1981,1802,3493,2543,4246,3356,4488,2975,4510,1955,2145,1485,4106,1506,3388,1504,4235,1585,2511,1797,3024,3117,2949,2728,3943,3961,3071,3256,2892,1881,3914,3520,3366,3684,4392,3288,4217,1617,3620,2458,1553,1817,3625,1575,2071,4061,3039,2865,2875,1940,1918,4138,3457,2352,3757,2479,4606,3565,2088,3589,4325,2818,3067,1913,2078,4419,1844,3874,2347,1654,2611,2325,4185,2743,2997,2490,4102,3346,4006,2226,1453,2643,4574,3593,3484,1508,4542,2971,3003,3368,2526,3729,3911,3613,2707,2988,2594,2174,2283,2389,2853,2290,2251,1903,2135,2406,4089,2554,1481,3383,1629,2004,3991,3748,3630,1854,4338,3561,3235,2431,4010,4495,2130,3859,2152,2262,4451,4261,3085,2009,3978,4197,3896,2576,3677,1607,2902,2315,1444,4306,3181,2384,2786,2796,4293,4175,3497,4153,3879,4214,3844,1777,4299,3598,1440,3149,3529,1706,3793,2680,2183,3351,3993,4074,4446,1893,2036,3645,2917,4372,3761,2779,2019,3420,1614,2374,2287,1642,1512,2683,3785,4254,3264,4523,2815,4367,3203,3164,3658,2123,1578,1957,4399,2155,2255,4356,3997,3907,3601,2233,3882,3987,3837,3464,2604,3790,3337,1673,1757,3496,4579,2768,1989,4350,4474,4007,2961,4034,3633,2619,2040,2668,3309,3982,2751,3956,4029,4178,4281,3347,1693,4083,4024,1561,2704,2913,2404,2714,3196,1891,3045,3506,2021,2063,4318,2549,1930,3244,3974,2966,1582,4484,4395,4019,3076,4501,2241,2127,2159,2810,4129,1829,1977,3057,2803,2847,3570,2485,3772,1550,4506,3259,4066,1500,3965,1923,4410,4206,3538,1925,4330,2539,1713,1597,2864,3740,1885,3812,3918,2270,4363,2372,3474,2879,3437,4274,4584,2881,3212,1463,3432,2453,3553,3721,3753,3901,3528,2754,2321,1944,4555,2206,1737,1681,3405,4161,2832,4547,2436,2438,1490,2297,4313,3443,1769,4423,4189,2170,2834,2191,1449,1468,2470,2980,3575,4552,2655,4002,1417,1870,3669,2771]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem  : SWV693-1 : TPTP v8.1.2. Released v4.1.0.
% 0.06/0.15  % Command  : run_Leo-III %s %d
% 0.16/0.36  % Computer : n021.cluster.edu
% 0.16/0.36  % Model    : x86_64 x86_64
% 0.16/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36  % Memory   : 8042.1875MB
% 0.16/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36  % CPULimit : 300
% 0.16/0.36  % WCLimit  : 300
% 0.16/0.36  % DateTime : Fri May 19 02:51:58 EDT 2023
% 0.16/0.36  % CPUTime  : 
% 0.98/0.85  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 2.04/1.15  % [INFO] 	 Parsing done (295ms). 
% 2.04/1.15  % [INFO] 	 Running in sequential loop mode. 
% 2.57/1.36  % [INFO] 	 eprover registered as external prover. 
% 2.57/1.36  % [INFO] 	 cvc4 registered as external prover. 
% 2.57/1.36  % [INFO] 	 Scanning for conjecture ... 
% 3.29/1.54  % [INFO] 	 Found a conjecture and 1470 axioms. Running axiom selection ... 
% 4.31/1.81  % [INFO] 	 Axiom selection finished. Selected 1412 axioms (removed 58 axioms). 
% 5.65/2.14  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.81/2.16  % [INFO] 	 Type checking passed. 
% 5.81/2.16  % [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 ... 
% 22.68/6.50  % External prover 'cvc4' found a proof!
% 22.68/6.50  % [INFO] 	 Killing All external provers ... 
% 22.68/6.50  % Time passed: 5973ms (effective reasoning time: 5343ms)
% 22.68/6.50  % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 22.68/6.51  % Axioms used in derivation (1412): cls_inf__sup__absorb_0, cls_Suc__pred_0, cls_divide__le__eq__number__of_9, cls_inf__sup__aci_I2_J_0, cls_root__cancel_0, cls_sumr__offset_0, cls_add__0__left_0, cls_le__divide__eq_8, cls_add__pos__nonneg_0, cls_LIMSEQ__diff_0, cls_power__0_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1, cls_le__divide__eq_3, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_less__divide__eq_3, cls_vimage__code_0, cls_divide__le__eq__number__of1_9, cls_Int__Un__distrib_0, cls_LIM__power_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_less__iff__diff__less__0_0, cls_differentiable__divide_0, cls_add__Suc__shift_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_one__le__mult__iff_1, cls_le__0__eq_1, cls_natgb_Oadd__r0__iff_1, cls_divide__eq__eq_3, cls_eq__add__iff2_1, 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_divide__le__eq_2, cls_Suc__inject_0, cls_eq__imp__le_0, cls_order__eq__iff_0, cls_divide__less__0__iff_0, cls_Suc__mono_0, cls_nat__0__less__mult__iff_1, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_le__diff__iff_0, cls_zero__less__divide__iff_5, cls_of__nat__0_0, cls_less__divide__eq__number__of1_6, cls_le__diff__conv_1, cls_sup__ge1_0, cls_of__nat__add_0, cls_differentiable__power_0, cls_divide__pos__pos_0, cls_mult__imp__le__div__pos_0, cls_class__ringb_Oadd__r0__iff_1, cls_mult__nonneg__nonneg_0, cls_mult__right_Osuminf_0, cls_eq__divide__eq__number__of1_4, cls_add__less__cancel__left_1, cls_mult__right__mono_0, cls_mult__right_Ozero_0, cls_DERIV__mult__lemma_0, cls_order__less__le__trans_0, cls_comm__semiring__class_Odistrib_0, cls_sums__diff_0, cls_insert__inter__insert_0, cls_divide__eq__eq__number__of_4, cls_le__add__diff__inverse2_0, cls_Nat_Odiff__diff__eq_0, cls_left__add__mult__distrib_0, cls_mult_Odiff__left_0, cls_divide__self_0, cls_DERIV__iff2_0, cls_mult__nonneg__nonpos2_0, cls_one__is__add_4, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_divide_Osuminf_0, cls_divide__le__eq__number__of_4, cls_LIMSEQ__diff__approach__zero2_0, clsarity_nat__Lattices_Odistrib__lattice, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, cls_inverse__zero__imp__zero_0, cls_xt1_I12_J_0, cls_COMBC__def_0, cls_mult__less__cancel__right__disj_0, cls_setsum__head__upt__Suc_0, cls_power__divides__special_0, cls_sum__squares__eq__zero__iff_0, cls_negative__imp__inverse__negative_0, cls_GCD__empty__nat_0, cls_Suc__n__not__n_0, cls_differentiable__mult_0, clsarity_Complex__Ocomplex__Int_Onumber, cls_divide__nonpos__neg_0, cls_lordered__ab__group__add__class_Oadd__sup__inf__distribs_I2_J_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_le__divide__eq__number__of1_0, cls_lemma__realpow__rev__sumr_0, cls_mult__less__cancel__left__disj_1, cls_sup__bot__right_0, cls_gcd__lcm__complete__lattice__nat_OSup__singleton_0, cls_zero__le__one_0, cls_insert__code_1, cls_Un__empty__left_0, cls_mult__is__0_2, cls_nat__add__left__cancel__less_1, cls_power__eq__0__iff_1, cls_termination__basic__simps_I5_J_0, cls_add__increasing2_0, cls_DERIV__diff_0, cls_less__antisym_0, cls_add__sup__distrib__right_0, cls_le__divide__eq__number__of_6, cls_right__distrib__number__of_0, cls_lemma__realpow__diff_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_pos__add__strict_0, cls_zero__le__divide__iff_2, cls_isCont__iff_1, cls_nat__lt__two__imp__zero__or__one_0, cls_eq__diff__iff_0, cls_DERIV__cmult_0, cls_inverse__eq__iff__eq_0, cls_assms_0, cls_less__half__sum_0, cls_LIMSEQ__inverse_0, clsarity_bool__Lattices_Olower__semilattice, cls_add__is__1_2, cls_distrib__sup__le_0, cls_LIMSEQ__divide_0, cls_power__inject__exp_0, cls_zero__le__mult__iff_3, cls_linorder__neqE_0, cls_divide__1_0, cls_add__strict__right__mono_0, cls_divide__less__eq__number__of1_5, cls_Zseq__mult__right_0, cls_le__iff__inf_1, cls_sums__mult2_0, cls_CHAINED_0, cls_power__increasing_0, cls_one__le__mult__iff_0, cls_inf__sup__aci_I6_J_0, cls_inverse__le__1__iff_2, cls_less__add__Suc2_0, cls_divide__le__eq__number__of1_4, cls_of__nat__less__iff_0, cls_DERIV__unique_0, cls_Un__commute_0, cls_less__divide__eq__number__of_8, cls_nonzero__inverse__eq__divide_0, clsarity_fun__Orderings_Oorder, cls_not__sum__squares__lt__zero_0, cls_power__le__zero__eq_3, cls_class__semiring_Osemiring__rules_I21_J_0, cls_zero__less__divide__iff_0, cls_divide__less__eq__number__of_1, cls_less__imp__inverse__less__neg_0, cls_add__is__0_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_divide__le__0__1__iff_1, cls_le__inf__iff_1, cls_divide__le__eq_7, cls_not__less__eq_1, cls_frac__le_0, cls_inverse__less__1__iff_2, cls_add__le__cancel__right_1, cls_one__le__inverse__iff_2, cls_inverse__1_0, cls_termination__basic__simps_I1_J_0, cls_divide__less__eq_4, cls_add__le__cancel__left_1, cls_divide__le__eq_8, cls_less__divide__eq__number__of_3, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__1, cls_LIMSEQ__setsum_1, cls_divide__less__eq__number__of1_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_le__divide__eq__number__of1_5, cls_Suc__lessI_0, cls_diff__cancel_0, cls_add__imp__eq_0, cls_nat__eq__add__iff1_0, cls_less__Suc__eq_2, cls_divide_OLIM_0, cls_tendsto__divide_0, cls_nat__add__left__cancel__less_0, cls_setsum__atMost__Suc_0, cls_less__supI1_0, cls_Int__Un__distrib2_0, cls_left__distrib__number__of_0, cls_one__is__add_1, cls_mult__nonpos__nonneg_0, cls_power__less__zero__eq_1, cls_inverse__negative__iff__negative_1, clsarity_nat__Orderings_Olinorder, cls_eq__divide__eq__number__of_4, cls_mult__nonpos__nonpos_0, cls_class__ringb_Onoteq__reduce_0, cls_Zseq__mult_0, cls_add__leE_0, cls_mult__less__imp__less__right_0, cls_Suc__mult__cancel1_0, cls_left__inverse_0, cls_comm__monoid__add_Omult__assoc_0, 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cls_divide__less__eq__number__of_2, cls_inverse__positive__imp__positive_0, cls_ivl__disj__int_I9_J_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_atLeastLessThan__add__Un_0, cls_less__divide__eq__number__of1_9, cls_DERIV__power_0, cls_sums__divide_0, cls_insert__code_0, cls_eq__divide__eq__number__of_0, cls_le__eqI_1, cls_class__semiring_Opwr__0_0, cls_Suc__diff__le_0, cls_mult__eq__0__iff_1, cls_le__iff__diff__le__0_1, cls_divide__nonpos__pos_0, cls_add__gr__0_2, cls_diff__le__mono_0, cls_add__less__le__mono_0, cls_power__increasing__iff_0, cls_divide__less__eq_3, clsarity_nat__Ring__and__Field_Osemiring__1, cls_nonzero__inverse__mult__distrib_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, cls_nonzero__power__inverse_0, cls_order__less__imp__le_0, cls_le__divide__eq__number__of1_4, clsarity_Complex__Ocomplex__RealVector_Oreal__field, cls_add__leE_1, cls_lemma__realpow__diff__sumr_0, cls_mult__cancel1_0, cls_atLeastLessThanSuc_1, cls_add__gr__0_1, cls_setsum__add__nat__ivl__singleton_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__0, cls_setsum__divide__distrib_0, cls_division__ring__inverse__diff_0, cls_le__divide__eq__number__of_4, cls_le__add1_0, cls_sup__inf__distrib1_0, cls_power__diff__rev__if_0, cls_suminf__divide_0, cls_monoid__add__class_Oadd__0__right_0, cls_of__nat__less__iff_1, cls_mult__idem_0, cls_le__infI2_0, cls_le__imp__inverse__le__neg_0, cls_less__divide__eq__number__of_5, cls_sup__bot__left_0, cls_diff__commute_0, cls_mult__left_Osuminf_0, cls_zero__le__divide__iff_1, cls_power__strict__increasing__iff_0, cls_Zfun__mult__left_0, cls_le__less__Suc__eq_1, cls_add__strict__increasing2_0, cls_le__add__diff_0, cls_less__Suc0_1, cls_mult__right_Otendsto_0, cls_divide__eq__eq_1, cls_le__divide__eq_5, cls_divide__less__eq__number__of1_1, cls_termination__basic__simps_I2_J_0, cls_of__nat__Suc_0, cls_class__ringb_Osubr0__iff_0, cls_le__eq__less__or__eq_0, cls_setsum__subtractf_0, cls_vimage__empty_0, cls_divide__le__eq__number__of1_0, clsarity_nat__Ring__and__Field_Omult__zero, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_DERIV__mult_H_0, cls_class__semiring_Omul__pwr_0, cls_setsum__op__ivl__Suc_1, cls_zero__less__power__eq__number__of_2, clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors, cls_eq__iff__diff__eq__0_0, cls_suminf__mult_0, cls_insert__commute_0, cls_isCont__def_1, cls_differentiableI_0, cls_sumr__diff__mult__const2_0, cls_xt1_I7_J_0, cls_less__divide__eq__number__of1_5, cls_mult__divide__mult__cancel__left_0, cls_mult__left_Ozero_0, cls_natgb_Oadd__mul__solve_1, cls_divide__less__eq__number__of_5, cls_power__decreasing_0, cls_zero__less__divide__1__iff_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_mult__le__0__iff_3, cls_inverse__nonpositive__iff__nonpositive_1, cls_nat__mult__less__cancel1_0, cls_nat__mult__eq__cancel__disj_0, cls_mult__neg__neg_0, cls_linorder__not__less_1, cls_zero__less__Suc_0, cls_mult__less__cancel__left__neg_0, cls_class__semiring_Osemiring__rules_I4_J_0, clsarity_Complex__Ocomplex__Int_Onumber__ring, cls_not__one__le__zero_0, cls_le__neq__implies__less_0, cls_le__add__iff2_0, cls_nat__less__le_1, cls_Un__insert__right_0, cls_mult__less__le__imp__less_0, cls_mult__le__less__imp__less_0, cls_inf__sup__distrib2_0, cls_ivl__disj__un_I17_J_0, cls_LIMSEQ__Zseq__iff_0, cls_divide__less__0__1__iff_1, clsarity_fun__Lattices_Odistrib__lattice, cls_add__le__cancel__left_0, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring, cls_tendsto__diff_0, cls_ivl__disj__un_I15_J_0, cls_le__divide__eq__number__of1_8, cls_power__Suc__less_0, cls_inf__bot__right_0, cls_sup__absorb1_0, cls_sums__add_0, cls_less__eqI_1, cls_atMost__0_0, cls_zero__le__imp__of__nat_0, cls_zero__le__divide__1__iff_0, cls_less__divide__eq_9, cls_le__refl_0, cls_less__divide__eq__number__of_9, cls_le__divide__eq__number__of_0, cls_mult__less__cancel__left__pos_0, cls_divide__less__0__iff_4, cls_inf1E_0, cls_nat__eq__add__iff2_1, cls_class__semiring_Osemiring__rules_I22_J_0, cls_power__mono_0, cls_zero__le__mult__iff_2, cls_even__less__0__iff_0, cls_le__SucI_0, cls_mult__left_Oadd_0, cls_mult__left_Osums_0, cls_suminf__mult2_0, cls_divide__le__eq__number__of_3, cls_not__less__eq__eq_0, cls_power__le__zero__eq__number__of_3, cls_power__0__left_1, cls_le__divide__eq__number__of_9, cls_sum__squares__le__zero__iff_0, cls_add__le__cancel__right_0, cls_mult__right_Odiff_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__cancel2_1, cls_mult__strict__left__mono__neg_0, cls_mult__eq__1__iff_2, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, cls_nat__add__commute_0, cls_Deriv_Oadd__diff__add_0, cls_split__mult__neg__le_1, cls_LIM__inverse_0, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring__0, cls_LIM__compose_0, cls_le__number__of__eq__not__less_0, cls_right__inverse__eq_1, cls_add__diff__inverse_0, cls_divide__le__eq__number__of_6, cls_less__divide__eq__number__of1_1, cls_divide__le__eq_1, cls_of__nat__less__0__iff_0, cls_root__summation_0, cls_divide__le__0__1__iff_0
% 22.68/6.51  % No. of inferences in proof: 2827
% 22.68/6.51  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 5973 ms resp. 5343 ms w/o parsing
% 23.84/7.01  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 23.84/7.03  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------