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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ALG400-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39

% Computer : n014.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8046.5625MB
% OS       : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Sun Sep 27 06:46:53 AM UTC 2026

% Result   : Unsatisfiable 92.13s 20.63s
% Output   : Refutation 95.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   30
%            Number of leaves      :  554
% Syntax   : Number of formulae    : 1613 ( 255 unt;   0 typ;   0 def)
%            Number of atoms       : 6005 ( 860 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives : 27816 (3623   ~;3848   |;   0   &;20345   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   23 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   60 (  57 usr;   6 con; 0-5 aty)
%            Number of variables   : 3548 (   0   ^;3548   !;   0   ?;3548   :)

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

thf(c_RealVector_Onorm__class_Onorm_decl,type,
    c_RealVector_Onorm__class_Onorm: $i > $i > $i ).

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

thf(c_Polynomial_Opoly_decl,type,
    c_Polynomial_Opoly: $i > $i > $i > $i ).

thf(v_q_____decl,type,
    v_q____: $i ).

thf(v_w_____decl,type,
    v_w____: $i ).

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

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

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

thf(tc_RealDef_Oreal_decl,type,
    tc_RealDef_Oreal: $i ).

thf(c_Polynomial_Osmult_decl,type,
    c_Polynomial_Osmult: $i > $i > $i > $i ).

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

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

thf(tc_Polynomial_Opoly_decl,type,
    tc_Polynomial_Opoly: $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_Polynomial_Opdivmod__rel_decl,type,
    c_Polynomial_Opdivmod__rel: $i > $i > $i > $i > $i > $o ).

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

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

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

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

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

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

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

thf(c_Divides_Odiv__class_Odiv_decl,type,
    c_Divides_Odiv__class_Odiv: $i > $i > $i > $i ).

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

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

thf(class_Int_Oring__char__0_decl,type,
    class_Int_Oring__char__0: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_RealVector_Oreal__normed__algebra__1_decl,type,
    class_RealVector_Oreal__normed__algebra__1: $i > $o ).

thf(c_Fundamental__Theorem__Algebra__Mirabelle_Opsize_decl,type,
    c_Fundamental__Theorem__Algebra__Mirabelle_Opsize: $i > $i > $i ).

thf(39,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oidom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oidom) ).

thf(645,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oidom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(393,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).

thf(1411,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(214,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).

thf(1024,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(291,axiom,
    tc_Complex_Ocomplex @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).

thf(1190,plain,
    tc_Complex_Ocomplex @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(544,axiom,
    ( ( tc_Complex_Ocomplex @ ( v_q____ @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
    = ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lgqr_0) ).

thf(1729,plain,
    ( ( tc_Complex_Ocomplex @ ( v_q____ @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) )
    = ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Fundamental__Theorem__Algebra__Mirabelle_Opsize ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(153,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero_0) ).

thf(893,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(349,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).

thf(1315,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(253,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).

thf(1110,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(523,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_1) ).

thf(1686,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).

thf(1337,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(539,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).

thf(1718,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(463,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).

thf(1559,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(251,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(1105,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(160,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).

thf(909,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(32,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(628,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(408,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0) ).

thf(1441,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).

thf(593,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(594,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(cnf,[status(esa)],[593]) ).

thf(5374,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[1441,594]) ).

thf(5375,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[5374]) ).

thf(5376,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[5375:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(5412,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[5376,594]) ).

thf(5413,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[5412]) ).

thf(5414,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[5413:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(5621,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[5414,594]) ).

thf(5622,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[5621]) ).

thf(5623,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[5622:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(6489,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[5623,594]) ).

thf(6490,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[6489]) ).

thf(6491,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[6490:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(7483,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[6491,594]) ).

thf(7484,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[7483]) ).

thf(7485,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[7484:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(8582,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[7485,594]) ).

thf(8583,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[8582]) ).

thf(8584,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[8583:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(9074,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[8584,594]) ).

thf(9075,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[9074]) ).

thf(9076,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[9075:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(240,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_6) ).

thf(1083,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(98,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(777,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(1,negated_conjecture,
    ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
    | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(555,plain,
    ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
    | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(48,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult) ).

thf(666,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(339,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).

thf(1295,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_1) ).

thf(1200,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(55,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict) ).

thf(683,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(76,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult1_0) ).

thf(730,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(149,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1) ).

thf(884,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(3,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1) ).

thf(559,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(560,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(cnf,[status(esa)],[559]) ).

thf(1794,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[884,560]) ).

thf(1795,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[1794]) ).

thf(1796,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[1795:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(2158,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[1796,560]) ).

thf(2159,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[2158]) ).

thf(2160,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[2159:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(4363,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[2160,560]) ).

thf(4364,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[4363]) ).

thf(4365,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[4364:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(14,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber) ).

thf(584,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(585,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(cnf,[status(esa)],[584]) ).

thf(5642,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[4365,585]) ).

thf(5643,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[5642]) ).

thf(5644,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[5643:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2,negated_conjecture,
    ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
    | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(556,plain,
    ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
    | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(558,plain,
    ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
    | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(cnf,[status(esa)],[556]) ).

thf(13,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom) ).

thf(582,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(583,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(cnf,[status(esa)],[582]) ).

thf(2144,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(paramod_ordered,[status(thm)],[909,583]) ).

thf(2145,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(simp,[status(thm)],[2144]) ).

thf(2146,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom,
    inference(pattern_uni,[status(thm)],[2145:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(265,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

thf(1136,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(1137,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(cnf,[status(esa)],[1136]) ).

thf(4251,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom )
       != ( A @ class_Ring__and__Field_Oordered__semidom ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2146,1137]) ).

thf(4252,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom )
       != ( A @ class_Ring__and__Field_Oordered__semidom ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[4251]) ).

thf(4253,plain,
    ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[4252:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(4410,plain,
    ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ) )
    | ~ $true
    | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(paramod_ordered,[status(thm)],[558,4253]) ).

thf(4411,plain,
    ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ) )
    | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[4410]) ).

thf(4444,plain,
    ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) )
    | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[4411]) ).

thf(6,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Oorder) ).

thf(566,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(567,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
    inference(cnf,[status(esa)],[566]) ).

thf(1826,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
    inference(paramod_ordered,[status(thm)],[909,567]) ).

thf(1827,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
    inference(simp,[status(thm)],[1826]) ).

thf(1828,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Orderings_Oorder,
    inference(pattern_uni,[status(thm)],[1827:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(271,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(1148,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(1149,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(cnf,[status(esa)],[1148]) ).

thf(2161,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Orderings_Oorder )
       != ( A @ class_Orderings_Oorder ) )
      | ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1828,1149]) ).

thf(2162,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Orderings_Oorder )
       != ( A @ class_Orderings_Oorder ) )
      | ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2161]) ).

thf(2163,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[2162:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly )),bind(B,$thf( B ))]]) ).

thf(2164,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[2163]) ).

thf(4759,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ $true
      | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
       != tc_RealDef_Oreal )
      | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) ) ),
    inference(paramod_ordered,[status(thm)],[4444,2164]) ).

thf(4760,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
       != tc_RealDef_Oreal )
      | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[4759]) ).

thf(4938,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
       != tc_RealDef_Oreal )
      | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
       != A )
      | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != A )
      | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
       != tc_RealDef_Oreal )
      | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[4760]) ).

thf(5000,plain,
    ( ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
    | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[4938]) ).

thf(298,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_5) ).

thf(1205,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(327,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

thf(1269,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(451,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).

thf(1533,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(406,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).

thf(1437,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(140,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_6) ).

thf(861,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(91,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict) ).

thf(762,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(303,axiom,
    tc_RealDef_Oreal @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).

thf(1215,plain,
    tc_RealDef_Oreal @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(11,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(578,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(579,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(cnf,[status(esa)],[578]) ).

thf(2106,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Orderings_Opreorder )
       != ( A @ class_Orderings_Opreorder ) )
      | ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1215,579]) ).

thf(2107,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Orderings_Opreorder )
       != ( A @ class_Orderings_Opreorder ) )
      | ( A @ ( B @ ( B @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[2106]) ).

thf(2108,plain,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ),
    inference(pattern_uni,[status(thm)],[2107:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(2117,plain,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ),
    inference(simp,[status(thm)],[2108]) ).

thf(390,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).

thf(1406,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(26,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict) ).

thf(613,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(614,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(cnf,[status(esa)],[613]) ).

thf(527,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_left__inverse_0) ).

thf(1692,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(344,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).

thf(1305,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(19,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).

thf(595,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(596,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[595]) ).

thf(597,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(lifteq,[status(thm)],[596]) ).

thf(399,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_2) ).

thf(1426,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(516,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( E @ ( D @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ( A @ ( A @ ( F @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( E @ ( B @ c_Polynomial_Osmult ) ) @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pdivmod__rel__smult__left_0) ).

thf(1671,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( F @ ( E @ ( D @ ( C @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ( A @ ( A @ ( F @ ( B @ c_Polynomial_Osmult ) ) @ ( A @ ( E @ ( B @ c_Polynomial_Osmult ) ) @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(509,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).

thf(1655,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(107,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0) ).

thf(797,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(348,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1) ).

thf(1314,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(1899,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[1314,560]) ).

thf(1900,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[1899]) ).

thf(1901,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[1900:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(2185,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[1901,560]) ).

thf(2186,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[2185]) ).

thf(2187,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[2186:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(4529,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[2187,560]) ).

thf(4530,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[4529]) ).

thf(4531,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[4530:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(5699,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[4531,585]) ).

thf(5700,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[5699]) ).

thf(5701,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[5700:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(323,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_0) ).

thf(1260,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(50,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(670,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(435,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
        = C )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_0) ).

thf(1497,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) )
        = C )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(533,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(1705,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(301,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).

thf(1212,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(369,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).

thf(1359,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(1360,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(cnf,[status(esa)],[1359]) ).

thf(1865,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semidom )
       != ( A @ class_Ring__and__Field_Oordered__semidom ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1212,1360]) ).

thf(1866,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semidom )
       != ( A @ class_Ring__and__Field_Oordered__semidom ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[1865]) ).

thf(1867,plain,
    ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ),
    inference(pattern_uni,[status(thm)],[1866:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(2182,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[1901,585]) ).

thf(2183,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[2182]) ).

thf(2184,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[2183:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(329,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).

thf(1275,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(335,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

thf(1288,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(12,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one) ).

thf(580,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(581,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(cnf,[status(esa)],[580]) ).

thf(1270,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(cnf,[status(esa)],[1269]) ).

thf(1271,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ozero__neq__one )
      | ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(lifteq,[status(thm)],[1270]) ).

thf(2127,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one )
       != ( B @ class_Ring__and__Field_Ozero__neq__one ) )
      | ~ $true
      | ( ( B @ c_HOL_Oone__class_Oone )
       != ( B @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(paramod_ordered,[status(thm)],[581,1271]) ).

thf(2128,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one )
       != ( B @ class_Ring__and__Field_Ozero__neq__one ) )
      | ( ( B @ c_HOL_Oone__class_Oone )
       != ( B @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[2127]) ).

thf(2129,plain,
    ! [A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
       != ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(pattern_uni,[status(thm)],[2128:[bind(A,$thf( C )),bind(B,$thf( C @ tc_Polynomial_Opoly ))]]) ).

thf(2133,plain,
    ! [A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
       != ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[2129]) ).

thf(2139,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
       != ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1288,2133]) ).

thf(2140,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
       != ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[2139]) ).

thf(2141,plain,
    ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
   != ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[2140:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(9,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero) ).

thf(573,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(574,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(cnf,[status(esa)],[573]) ).

thf(15914,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[9076,574]) ).

thf(15915,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[15914]) ).

thf(15916,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[15915:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(361,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(1342,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).

thf(747,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(306,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).

thf(1222,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(171,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).

thf(930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(123,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).

thf(829,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(154,axiom,
    ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) )
   != ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_a00_0) ).

thf(896,plain,
    ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) )
   != ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(897,plain,
    ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) )
   != ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
    inference(polarity_switch,[status(thm)],[896]) ).

thf(898,plain,
    ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) )
   != ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
    inference(lifteq,[status(thm)],[897]) ).

thf(5371,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[797,594]) ).

thf(5372,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[5371]) ).

thf(5373,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[5372:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(5394,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[5373,594]) ).

thf(5395,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[5394]) ).

thf(5396,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[5395:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(5448,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[5396,594]) ).

thf(5449,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[5448]) ).

thf(5450,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[5449:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(6171,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[5450,594]) ).

thf(6172,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[6171]) ).

thf(6173,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[6172:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(7062,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[6173,574]) ).

thf(7063,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[7062]) ).

thf(7064,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[7063:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(67,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).

thf(709,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(381,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( F @ ( E @ ( D @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ( A @ ( F @ ( A @ ( E @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pdivmod__rel__smult__right_0) ).

thf(1386,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( F @ ( E @ ( D @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ( A @ ( F @ ( A @ ( E @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(542,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).

thf(1724,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(325,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).

thf(1265,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(5391,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[5373,574]) ).

thf(5392,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[5391]) ).

thf(5393,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[5392:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(261,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_1) ).

thf(1127,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(383,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide__number__of_0) ).

thf(1391,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(471,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(1576,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(192,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult1__if_0) ).

thf(973,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(150,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_0) ).

thf(885,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(506,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(1650,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(17,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).

thf(591,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(592,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(cnf,[status(esa)],[591]) ).

thf(5721,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[4531,592]) ).

thf(5722,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[5721]) ).

thf(5723,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[5722:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(5,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult) ).

thf(564,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(565,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult ) ),
    inference(cnf,[status(esa)],[564]) ).

thf(372,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_2) ).

thf(1366,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(493,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_3) ).

thf(1623,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(427,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).

thf(1482,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(320,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).

thf(1254,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(496,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self_0) ).

thf(1628,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(535,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).

thf(1709,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(8,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

thf(570,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(402,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

thf(1430,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(356,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_3) ).

thf(1330,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(86,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__1_0) ).

thf(751,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).

thf(802,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(332,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(1279,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(414,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).

thf(1455,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(292,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).

thf(1191,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(440,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).

thf(1508,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(2124,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(paramod_ordered,[status(thm)],[1508,581]) ).

thf(2125,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(simp,[status(thm)],[2124]) ).

thf(2126,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one,
    inference(pattern_uni,[status(thm)],[2125:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(179,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_8) ).

thf(949,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(353,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_7) ).

thf(1323,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(28,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(617,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(618,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(cnf,[status(esa)],[617]) ).

thf(619,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder )
      | ( B = C ) ),
    inference(lifteq,[status(thm)],[618]) ).

thf(127,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_1) ).

thf(838,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(229,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).

thf(1059,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(263,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).

thf(1132,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(118,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).

thf(817,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(378,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).

thf(1379,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(443,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).

thf(1514,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(317,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_0) ).

thf(1247,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(469,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).

thf(1572,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(95,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).

thf(770,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(386,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

thf(1398,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(5050,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[2187,592]) ).

thf(5051,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[5050]) ).

thf(5052,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[5051:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(557,plain,
    ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
    | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(cnf,[status(esa)],[555]) ).

thf(4769,plain,
    ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) )
    | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
    | ~ $true
    | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) ) ),
    inference(paramod_ordered,[status(thm)],[4444,557]) ).

thf(4770,plain,
    ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) )
    | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
    | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[4769]) ).

thf(4771,plain,
    ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
    | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) ) ),
    inference(pattern_uni,[status(thm)],[4770:[]]) ).

thf(33,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict) ).

thf(631,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(632,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(cnf,[status(esa)],[631]) ).

thf(17589,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(paramod_ordered,[status(thm)],[909,632]) ).

thf(17590,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(simp,[status(thm)],[17589]) ).

thf(17591,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__ring__strict,
    inference(pattern_uni,[status(thm)],[17590:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(5661,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[4365,560]) ).

thf(5662,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[5661]) ).

thf(5663,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[5662:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(6569,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[5663,560]) ).

thf(6570,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[6569]) ).

thf(6571,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[6570:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(7579,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[6571,560]) ).

thf(7580,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[7579]) ).

thf(7581,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[7580:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(8698,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[7581,560]) ).

thf(8699,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[8698]) ).

thf(8700,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[8699:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(13893,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[8700,560]) ).

thf(13894,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[13893]) ).

thf(13895,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[13894:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(36,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( G @ ( B @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ~ ( A @ ( F @ ( C @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ( B = C )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pdivmod__rel__unique_0) ).

thf(638,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( G @ ( B @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ~ ( A @ ( F @ ( C @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ( B = C )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(136,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).

thf(853,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(351,axiom,
    tc_RealDef_Oreal @ class_Int_Onumber__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).

thf(1319,plain,
    tc_RealDef_Oreal @ class_Int_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(1888,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult ) ),
    inference(paramod_ordered,[status(thm)],[1288,565]) ).

thf(1889,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult ) ),
    inference(simp,[status(thm)],[1888]) ).

thf(1890,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult,
    inference(pattern_uni,[status(thm)],[1889:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(426,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( E
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).

thf(1479,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( E
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(487,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).

thf(1609,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(501,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

thf(1641,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(8701,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[7581,592]) ).

thf(8702,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[8701]) ).

thf(8703,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[8702:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(310,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_1) ).

thf(1232,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(431,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(1489,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(168,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).

thf(924,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(419,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).

thf(1465,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(537,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_4) ).

thf(1714,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(221,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_3) ).

thf(1040,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(5718,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[4531,560]) ).

thf(5719,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[5718]) ).

thf(5720,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[5719:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(6928,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[5720,560]) ).

thf(6929,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[6928]) ).

thf(6930,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[6929:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(8228,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[6930,560]) ).

thf(8229,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[8228]) ).

thf(8230,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[8229:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(8856,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[8230,560]) ).

thf(8857,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[8856]) ).

thf(8858,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[8857:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(14405,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[8858,560]) ).

thf(14406,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[14405]) ).

thf(14407,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[14406:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(16691,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[14407,592]) ).

thf(16692,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[16691]) ).

thf(16693,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[16692:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(158,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_2) ).

thf(905,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(88,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).

thf(756,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(513,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_0) ).

thf(1664,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(521,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).

thf(1682,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).

thf(113,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).

thf(806,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(473,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).

thf(1581,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).

thf(966,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).

thf(692,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(384,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).

thf(1394,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(365,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).

thf(1351,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I7_J_0) ).

thf(660,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(198,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( E @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less2_0) ).

thf(988,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( E @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(404,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).

thf(1433,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(483,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_3) ).

thf(1600,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(21,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).

thf(600,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(601,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[600]) ).

thf(602,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(lifteq,[status(thm)],[601]) ).

thf(5057,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[1314,592]) ).

thf(5058,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[5057]) ).

thf(5059,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[5058:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(281,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__mult2_0) ).

thf(1169,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(57,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_4) ).

thf(687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(34,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom) ).

thf(633,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(634,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom ) ),
    inference(cnf,[status(esa)],[633]) ).

thf(14370,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[8858,585]) ).

thf(14371,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[14370]) ).

thf(14372,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[14371:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(183,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).

thf(956,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(14408,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[8858,592]) ).

thf(14409,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[14408]) ).

thf(14410,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[14409:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(142,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).

thf(866,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(234,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(1072,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(529,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).

thf(1697,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(315,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).

thf(1242,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(2150,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom )
       != ( B @ class_Ring__and__Field_Oordered__semidom ) )
      | ~ ( B @ ( B @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ $true
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[583,1360]) ).

thf(2151,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom )
       != ( B @ class_Ring__and__Field_Oordered__semidom ) )
      | ~ ( B @ ( B @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2150]) ).

thf(2152,plain,
    ! [A: $i] :
      ( ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[2151:[bind(A,$thf( C )),bind(B,$thf( C @ tc_Polynomial_Opoly ))]]) ).

thf(2154,plain,
    ! [A: $i] :
      ( ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2152]) ).

thf(446,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_9) ).

thf(1521,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(235,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_right__inverse_0) ).

thf(1074,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(166,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).

thf(920,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(176,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_7) ).

thf(942,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(526,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Omult__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).

thf(1691,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(105,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).

thf(793,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(8825,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[8230,585]) ).

thf(8826,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[8825]) ).

thf(8827,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[8826:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(22,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(603,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(604,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(cnf,[status(esa)],[603]) ).

thf(4254,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom )
       != ( A @ class_Ring__and__Field_Oordered__semidom ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2146,1360]) ).

thf(4255,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom )
       != ( A @ class_Ring__and__Field_Oordered__semidom ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[4254]) ).

thf(4256,plain,
    ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ),
    inference(pattern_uni,[status(thm)],[4255:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(6849,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_lessequals ) ) )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) )
      | ~ $true
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(paramod_ordered,[status(thm)],[604,4256]) ).

thf(6850,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_lessequals ) ) )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(simp,[status(thm)],[6849]) ).

thf(6851,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
    inference(pattern_uni,[status(thm)],[6850:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly )),bind(B,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )),bind(C,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero )),bind(D,$thf( D ))]]) ).

thf(6868,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
    inference(simp,[status(thm)],[6851]) ).

thf(8396,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ $true ),
    inference(rewrite,[status(thm)],[6868,1828]) ).

thf(8397,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[8396]) ).

thf(6834,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_lessequals ) ) )
       != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) )
      | ~ $true
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(paramod_ordered,[status(thm)],[604,1867]) ).

thf(6835,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_lessequals ) ) )
       != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(simp,[status(thm)],[6834]) ).

thf(6836,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ class_Orderings_Oorder ) ),
    inference(pattern_uni,[status(thm)],[6835:[bind(A,$thf( tc_RealDef_Oreal )),bind(B,$thf( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )),bind(C,$thf( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )),bind(D,$thf( D ))]]) ).

thf(6869,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ class_Orderings_Oorder ) ),
    inference(simp,[status(thm)],[6836]) ).

thf(135,axiom,
    tc_RealDef_Oreal @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).

thf(852,plain,
    tc_RealDef_Oreal @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(7004,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ $true ),
    inference(rewrite,[status(thm)],[6869,852]) ).

thf(7005,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[7004]) ).

thf(7065,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[6173,594]) ).

thf(7066,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[7065]) ).

thf(7067,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[7066:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(8479,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[7067,594]) ).

thf(8480,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[8479]) ).

thf(8481,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[8480:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(499,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).

thf(1636,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(8231,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[6930,592]) ).

thf(8232,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[8231]) ).

thf(8233,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[8232:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(5409,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[5376,574]) ).

thf(5410,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[5409]) ).

thf(5411,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[5410:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(422,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_4) ).

thf(1470,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(232,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).

thf(1067,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(548,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).

thf(1736,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(69,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_2) ).

thf(714,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(31,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__idem_0) ).

thf(625,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(626,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(cnf,[status(esa)],[625]) ).

thf(627,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult )
      | ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B ) ),
    inference(lifteq,[status(thm)],[626]) ).

thf(432,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).

thf(1491,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(1492,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(cnf,[status(esa)],[1491]) ).

thf(17619,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__ring__strict )
       != ( A @ class_Ring__and__Field_Oordered__ring__strict ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[17591,1492]) ).

thf(17620,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__ring__strict )
       != ( A @ class_Ring__and__Field_Oordered__ring__strict ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[17619]) ).

thf(17621,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[17620:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly )),bind(B,$thf( B ))]]) ).

thf(17632,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[17621]) ).

thf(18062,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(paramod_ordered,[status(thm)],[627,17632]) ).

thf(18063,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(pattern_uni,[status(thm)],[18062:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

thf(18112,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(simp,[status(thm)],[18063]) ).

thf(224,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).

thf(1047,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(108,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

thf(798,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(278,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_5) ).

thf(1163,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(5047,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[1901,592]) ).

thf(5048,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[5047]) ).

thf(5049,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[5048:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(161,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).

thf(910,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(83,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).

thf(746,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(213,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_4) ).

thf(1021,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(222,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__smult__right_0) ).

thf(1042,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ tc_Polynomial_Opoly @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( B @ c_Divides_Odiv__class_Odiv ) ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(445,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).

thf(1519,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(367,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_6) ).

thf(1355,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(4,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).

thf(561,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(429,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ofield,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).

thf(1487,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ofield,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(313,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).

thf(1238,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(468,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).

thf(1570,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(283,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).

thf(1174,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(20,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ofield )
      | ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Divides_Osemiring__div) ).

thf(598,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ofield )
      | ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(16203,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[13895,585]) ).

thf(16204,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[16203]) ).

thf(16205,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[16204:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(437,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).

thf(1502,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(119,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).

thf(820,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(103,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).

thf(788,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(491,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

thf(1619,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(374,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).

thf(1370,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(117,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).

thf(815,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(2130,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(paramod_ordered,[status(thm)],[1288,581]) ).

thf(2131,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(simp,[status(thm)],[2130]) ).

thf(2132,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one,
    inference(pattern_uni,[status(thm)],[2131:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(13858,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[8700,585]) ).

thf(13859,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[13858]) ).

thf(13860,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[13859:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(164,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(916,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(27,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring) ).

thf(615,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(616,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring ) ),
    inference(cnf,[status(esa)],[615]) ).

thf(8918,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring ) ),
    inference(paramod_ordered,[status(thm)],[909,616]) ).

thf(8919,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring ) ),
    inference(simp,[status(thm)],[8918]) ).

thf(8920,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring,
    inference(pattern_uni,[status(thm)],[8919:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(147,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

thf(879,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(285,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

thf(1178,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(415,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(1457,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(276,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).

thf(1159,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(300,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_4) ).

thf(1210,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(237,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_8) ).

thf(1079,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(89,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).

thf(757,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(294,axiom,
    ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) )
   != ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(1195,plain,
    ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) )
   != ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(498,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).

thf(1634,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(337,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).

thf(1291,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(208,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).

thf(1012,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(132,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).

thf(847,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(218,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_Osmult ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__1__left_0) ).

thf(1032,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_Polynomial_Osmult ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(484,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__unique_0) ).

thf(1602,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = C )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(461,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).

thf(1555,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(550,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).

thf(1740,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(129,axiom,
    tc_RealDef_Oreal @ class_Int_Onumber,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber) ).

thf(842,plain,
    tc_RealDef_Oreal @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(388,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).

thf(1402,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(318,axiom,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_1) ).

thf(1249,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(1250,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(polarity_switch,[status(thm)],[1249]) ).

thf(1769,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ $true
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(paramod_ordered,[status(thm)],[558,1250]) ).

thf(1770,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1769]) ).

thf(1771,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
       != A )
      | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != A )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1770]) ).

thf(1772,plain,
    ( ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
    | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1771]) ).

thf(4757,plain,
    ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ) )
    | ~ $true
    | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) ) ),
    inference(paramod_ordered,[status(thm)],[4444,4253]) ).

thf(4758,plain,
    ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ) )
    | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[4757]) ).

thf(4942,plain,
    ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) )
    | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[4758]) ).

thf(5006,plain,
    ( ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) )
    | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[4942]) ).

thf(355,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).

thf(1328,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(1759,plain,
    ( ~ $true
    | ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) )
    | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[558]) ).

thf(1762,plain,
    ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) ) )
    | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1759]) ).

thf(1764,plain,
    ( ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) ) )
    | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1762]) ).

thf(1750,plain,
    ( ~ $true
    | ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) )
    | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(eqfactor_ordered,[status(thm)],[557]) ).

thf(1752,plain,
    ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) ) )
    | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1750]) ).

thf(1753,plain,
    ( ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) ) )
    | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1752]) ).

thf(7664,plain,
    ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) ) )
    | ~ $true
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1764,1753]) ).

thf(7665,plain,
    ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) ) ) ),
    inference(simp,[status(thm)],[7664]) ).

thf(7666,plain,
    ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
   != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) ) ),
    inference(pattern_uni,[status(thm)],[7665:[]]) ).

thf(7950,plain,
    ( ( tc_Complex_Ocomplex != tc_Complex_Ocomplex )
    | ( ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
     != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) ) ),
    inference(simp,[status(thm)],[7666]) ).

thf(8017,plain,
    ( ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
   != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) ),
    inference(simp,[status(thm)],[7950]) ).

thf(10730,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C != tc_Complex_Ocomplex )
      | ( ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( B @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
       != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(paramod_ordered,[status(thm)],[619,8017]) ).

thf(10731,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( B @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
       != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ ( tc_Complex_Ocomplex @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( tc_Complex_Ocomplex @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(pattern_uni,[status(thm)],[10730:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( tc_Complex_Ocomplex ))]]) ).

thf(247,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).

thf(1096,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(206,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__divide_0) ).

thf(1006,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(266,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).

thf(1138,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

thf(608,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(609,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(cnf,[status(esa)],[608]) ).

thf(610,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_OrderedGroup_Oab__semigroup__mult )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(lifteq,[status(thm)],[609]) ).

thf(257,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le__neg_0) ).

thf(1118,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(138,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).

thf(857,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(480,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).

thf(1592,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(81,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(742,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(1234,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(455,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).

thf(1541,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(145,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).

thf(874,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(269,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).

thf(1143,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(9071,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[8584,574]) ).

thf(9072,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[9071]) ).

thf(9073,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[9072:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(1968,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[1441,574]) ).

thf(1969,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[1968]) ).

thf(1970,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[1969:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(308,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).

thf(1227,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(195,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__smult__left_0) ).

thf(980,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ ( A @ tc_Polynomial_Opoly @ ( D @ ( C @ c_Divides_Odiv__class_Odiv ) ) @ ( B @ c_Polynomial_Osmult ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(477,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_8) ).

thf(1587,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(467,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_2) ).

thf(1567,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(433,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).

thf(1493,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(370,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).

thf(1361,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(511,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).

thf(1659,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(287,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_0) ).

thf(1182,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(417,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_8) ).

thf(1461,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(5618,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[5414,574]) ).

thf(5619,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[5618]) ).

thf(5620,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[5619:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(156,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__left_0) ).

thf(901,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(398,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).

thf(1424,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(475,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

thf(1584,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(530,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).

thf(1700,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(503,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_0) ).

thf(1644,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(552,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).

thf(1744,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(396,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_6) ).

thf(1419,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(216,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).

thf(1028,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(239,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).

thf(1082,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(338,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_3) ).

thf(1292,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = B )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(172,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).

thf(933,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(210,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).

thf(1016,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(299,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(1207,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( C = B )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(16,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).

thf(589,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(590,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    inference(cnf,[status(esa)],[589]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(679,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(190,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).

thf(970,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(66,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__norm__inverse_0) ).

thf(706,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(30,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
        = D )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__poly__eq_0) ).

thf(622,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
        = D )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(255,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_7) ).

thf(1114,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(701,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(340,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).

thf(1297,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(412,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_5) ).

thf(1451,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(16688,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[14407,560]) ).

thf(16689,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[16688]) ).

thf(16690,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[16689:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2147,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom )
       != ( B @ class_Ring__and__Field_Oordered__semidom ) )
      | ~ ( B @ ( B @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[583,1137]) ).

thf(2148,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom )
       != ( B @ class_Ring__and__Field_Oordered__semidom ) )
      | ~ ( B @ ( B @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2147]) ).

thf(2149,plain,
    ! [A: $i] :
      ( ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[2148:[bind(A,$thf( C )),bind(B,$thf( C @ tc_Polynomial_Opoly ))]]) ).

thf(2153,plain,
    ! [A: $i] :
      ( ~ ( A @ tc_Polynomial_Opoly @ ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2149]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono) ).

thf(654,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(225,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).

thf(1050,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(540,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_7) ).

thf(1720,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(99,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).

thf(779,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

thf(605,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(448,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).

thf(1525,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(40,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(647,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(324,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).

thf(1263,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(997,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(249,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).

thf(1099,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oinverse__class_Oinverse ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(197,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).

thf(985,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(272,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_1) ).

thf(1150,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(450,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).

thf(1530,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(454,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).

thf(1539,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(379,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).

thf(1382,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(204,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).

thf(1002,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(1850,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semidom )
       != ( A @ class_Ring__and__Field_Oordered__semidom ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1212,1137]) ).

thf(1851,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semidom )
       != ( A @ class_Ring__and__Field_Oordered__semidom ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1850]) ).

thf(1852,plain,
    ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[1851:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(7,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring) ).

thf(568,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(569,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(cnf,[status(esa)],[568]) ).

thf(401,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__cancel__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).

thf(1429,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(357,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_7) ).

thf(1333,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(528,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).

thf(1695,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(465,axiom,
    ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
    = ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r01_0) ).

thf(1563,plain,
    ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
    = ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(290,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(1187,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(490,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(1616,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(181,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__ring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).

thf(953,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__ring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(71,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_2) ).

thf(718,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(169,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_4) ).

thf(926,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(242,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_1) ).

thf(1086,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(174,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).

thf(938,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(93,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_7) ).

thf(765,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(227,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).

thf(1054,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(5445,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[5396,574]) ).

thf(5446,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[5445]) ).

thf(5447,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[5446:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(219,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_2) ).

thf(1035,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(420,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).

thf(1466,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(215,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_8) ).

thf(1026,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(280,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_0) ).

thf(1167,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(106,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).

thf(794,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(15,axiom,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( G @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ~ ( A @ ( C @ ( F @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ( B = C )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pdivmod__rel__unique_1) ).

thf(586,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( G @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ~ ( A @ ( C @ ( F @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ( B = C )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(331,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).

thf(1278,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(505,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).

thf(1648,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(5664,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[4365,592]) ).

thf(5665,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[5664]) ).

thf(5666,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[5665:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(319,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

thf(1251,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(599,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ofield )
      | ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
    inference(cnf,[status(esa)],[598]) ).

thf(6051,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ofield )
       != ( A @ class_Ring__and__Field_Ofield ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
    inference(paramod_ordered,[status(thm)],[1487,599]) ).

thf(6052,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ofield )
       != ( A @ class_Ring__and__Field_Ofield ) )
      | ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
    inference(simp,[status(thm)],[6051]) ).

thf(6053,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div,
    inference(pattern_uni,[status(thm)],[6052:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(270,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).

thf(1146,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(520,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono1_0) ).

thf(1680,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Omult__mono1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(458,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).

thf(1548,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(29,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring) ).

thf(620,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(621,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(cnf,[status(esa)],[620]) ).

thf(14301,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(paramod_ordered,[status(thm)],[909,621]) ).

thf(14302,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(simp,[status(thm)],[14301]) ).

thf(14303,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(pattern_uni,[status(thm)],[14302:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_0) ).

thf(1301,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(305,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
        = B )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__1_0) ).

thf(1219,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
        = B )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(824,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(553,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ozero__neq__one,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).

thf(1747,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(376,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__one__le_0) ).

thf(1374,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( C @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(497,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__divide_0) ).

thf(1631,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(5041,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[884,592]) ).

thf(5042,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[5041]) ).

thf(5043,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[5042:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(77,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).

thf(733,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(157,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).

thf(904,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(60,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

thf(694,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__comm__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(382,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_1) ).

thf(1389,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(96,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).

thf(772,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(13896,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[8700,592]) ).

thf(13897,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[13896]) ).

thf(13898,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[13897:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(507,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).

thf(1652,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(452,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).

thf(1535,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(184,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

thf(958,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(274,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).

thf(1154,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(8984,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[8481,594]) ).

thf(8985,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[8984]) ).

thf(8986,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[8985:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(14645,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[8986,574]) ).

thf(14646,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[14645]) ).

thf(14647,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[14646:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(130,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).

thf(843,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(260,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).

thf(1125,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(122,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

thf(826,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

thf(575,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(576,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[575]) ).

thf(577,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(lifteq,[status(thm)],[576]) ).

thf(68,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(711,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(531,axiom,
    tc_Complex_Ocomplex @ class_Int_Onumber,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).

thf(1701,plain,
    tc_Complex_Ocomplex @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(8579,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[7485,574]) ).

thf(8580,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[8579]) ).

thf(8581,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[8580:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(321,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( E @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__less_0) ).

thf(1256,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( E @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(430,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).

thf(1488,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(515,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_4) ).

thf(1669,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(15917,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[9076,594]) ).

thf(15918,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[15917]) ).

thf(15919,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[15918:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(571,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[570]) ).

thf(572,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(lifteq,[status(thm)],[571]) ).

thf(534,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_5) ).

thf(1707,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(347,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).

thf(1312,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(25,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1) ).

thf(611,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(546,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__field,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).

thf(1733,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(245,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).

thf(1092,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(244,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).

thf(1090,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(112,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).

thf(804,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(178,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).

thf(947,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(518,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

thf(1675,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(7480,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[6491,574]) ).

thf(7481,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[7480]) ).

thf(7482,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[7481:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(37,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Oring__char__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Oring__char__0) ).

thf(641,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Oring__char__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(400,axiom,
    tc_RealDef_Oreal @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).

thf(1428,plain,
    tc_RealDef_Oreal @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(322,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).

thf(1258,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(612,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono1 ) ),
    inference(cnf,[status(esa)],[611]) ).

thf(8522,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono1 ) ),
    inference(paramod_ordered,[status(thm)],[909,612]) ).

thf(8523,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono1 ) ),
    inference(simp,[status(thm)],[8522]) ).

thf(8524,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__mono1,
    inference(pattern_uni,[status(thm)],[8523:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(65,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).

thf(704,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(2109,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_lessequals ) ) )
       != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) )
      | ~ $true
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(paramod_ordered,[status(thm)],[579,1867]) ).

thf(2110,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_lessequals ) ) )
       != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(simp,[status(thm)],[2109]) ).

thf(2113,plain,
    ! [B: $i,A: $i] :
      ( ( A != tc_RealDef_Oreal )
      | ( B
       != ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( B
       != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(simp,[status(thm)],[2110]) ).

thf(2115,plain,
    ( ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
    | ~ ( tc_RealDef_Oreal @ class_Orderings_Opreorder ) ),
    inference(simp,[status(thm)],[2113]) ).

thf(2118,plain,
    ( ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
    | ~ $true ),
    inference(rewrite,[status(thm)],[2115,1215]) ).

thf(2119,plain,
    ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
   != ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
    inference(simp,[status(thm)],[2118]) ).

thf(124,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).

thf(831,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(333,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).

thf(1282,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(101,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_1) ).

thf(784,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(470,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(1574,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(541,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__imp__le_0) ).

thf(1722,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(2111,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_lessequals ) ) )
       != ( C @ ( C @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) )
      | ~ $true
      | ~ ( C @ class_Ring__and__Field_Oordered__semidom )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(paramod_ordered,[status(thm)],[579,1360]) ).

thf(2112,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_lessequals ) ) )
       != ( C @ ( C @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oone__class_Oone @ c_lessequals ) ) ) )
      | ~ ( C @ class_Ring__and__Field_Oordered__semidom )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(simp,[status(thm)],[2111]) ).

thf(2114,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A != C )
      | ( B
       != ( C @ c_HOL_Ozero__class_Ozero ) )
      | ( B
       != ( C @ c_HOL_Oone__class_Oone ) )
      | ~ ( C @ class_Ring__and__Field_Oordered__semidom )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(simp,[status(thm)],[2112]) ).

thf(2116,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(simp,[status(thm)],[2114]) ).

thf(79,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(737,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(525,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).

thf(1690,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(345,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).

thf(1307,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(141,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B = C )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).

thf(863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B = C )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(54,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(681,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(391,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).

thf(1408,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(478,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).

thf(1589,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(199,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).

thf(990,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

thf(649,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(259,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_3) ).

thf(1122,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(377,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(1376,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(407,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).

thf(1439,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).

thf(811,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(2199,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom )
       != ( B @ class_Ring__and__Field_Oordered__semidom ) )
      | ( ( B @ c_HOL_Oone__class_Oone )
       != ( B @ c_HOL_Ozero__class_Ozero ) )
      | ~ $true
      | ~ ( B @ class_Orderings_Opreorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[583,2116]) ).

thf(2200,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom )
       != ( B @ class_Ring__and__Field_Oordered__semidom ) )
      | ( ( B @ c_HOL_Oone__class_Oone )
       != ( B @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( B @ class_Orderings_Opreorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2199]) ).

thf(2201,plain,
    ! [A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
       != ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[2200:[bind(A,$thf( C )),bind(B,$thf( C @ tc_Polynomial_Opoly ))]]) ).

thf(2205,plain,
    ! [A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
       != ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2201]) ).

thf(6140,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder )
       != ( B @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) )
      | ( ( B @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
       != ( B @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ~ $true
      | ~ ( B @ class_Ring__and__Field_Oordered__idom )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[590,2205]) ).

thf(6141,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder )
       != ( B @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) )
      | ( ( B @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
       != ( B @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[6140]) ).

thf(6142,plain,
    ! [A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
       != ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[6141:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).

thf(6165,plain,
    ! [A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
       != ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[6142]) ).

thf(462,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).

thf(1557,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(8981,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[8481,574]) ).

thf(8982,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[8981]) ).

thf(8983,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[8982:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(133,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_4) ).

thf(848,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(354,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).

thf(1325,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(362,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).

thf(1344,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(49,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oidom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ono__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors) ).

thf(668,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oidom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ono__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(524,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).

thf(1688,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).

thf(152,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).

thf(890,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(514,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).

thf(1667,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(360,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

thf(1339,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(4408,plain,
    ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ) )
    | ~ $true
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
    inference(paramod_ordered,[status(thm)],[1772,4253]) ).

thf(4409,plain,
    ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[4408]) ).

thf(4445,plain,
    ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[4409]) ).

thf(545,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_8) ).

thf(1731,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(109,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).

thf(799,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(74,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).

thf(726,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(187,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_0) ).

thf(964,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(196,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).

thf(983,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(1924,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[797,574]) ).

thf(1925,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[1924]) ).

thf(1926,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[1925:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(424,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = C )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).

thf(1474,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = C )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(481,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero_0) ).

thf(1594,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(302,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).

thf(1213,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(425,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_3) ).

thf(1477,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(250,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).

thf(1102,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Olinorder) ).

thf(658,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(18182,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ $true
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__idem__mult )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(paramod_ordered,[status(thm)],[558,18112]) ).

thf(18183,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__idem__mult )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[18182]) ).

thf(18219,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
       != tc_RealDef_Oreal )
      | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != A )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__idem__mult )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[18183]) ).

thf(18240,plain,
    ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
    | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__idem__mult )
    | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[18219]) ).

thf(18481,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ $true
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__idem__mult )
      | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
       != tc_RealDef_Oreal )
      | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(paramod_ordered,[status(thm)],[18240,18112]) ).

thf(18482,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
       != tc_RealDef_Oreal )
      | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(simp,[status(thm)],[18481]) ).

thf(18639,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
       != tc_RealDef_Oreal )
      | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != A )
      | ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
       != tc_RealDef_Oreal )
      | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
       != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(simp,[status(thm)],[18482]) ).

thf(18715,plain,
    ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly )
     != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
     != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
    | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(simp,[status(thm)],[18639]) ).

thf(162,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_4) ).

thf(912,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(56,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oidom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors) ).

thf(685,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oidom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(295,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_2) ).

thf(1198,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(385,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_0) ).

thf(1396,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(6572,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[5663,592]) ).

thf(6573,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[6572]) ).

thf(6574,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[6573:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(185,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_0) ).

thf(959,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(2169,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[1796,585]) ).

thf(2170,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[2169]) ).

thf(2171,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[2170:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(6905,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[5720,585]) ).

thf(6906,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[6905]) ).

thf(6907,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[6906:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(316,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).

thf(1245,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(410,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__inverse_0) ).

thf(1445,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(143,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).

thf(868,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(284,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).

thf(1176,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(254,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

thf(1113,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(562,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[561]) ).

thf(563,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(lifteq,[status(thm)],[562]) ).

thf(1773,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one )
       != ( A @ class_Ring__and__Field_Ozero__neq__one ) )
      | ~ $true
      | ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(paramod_ordered,[status(thm)],[793,1271]) ).

thf(1774,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one )
       != ( A @ class_Ring__and__Field_Ozero__neq__one ) )
      | ( ( A @ c_HOL_Oone__class_Oone )
       != ( A @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[1773]) ).

thf(1775,plain,
    ( ( tc_Complex_Ocomplex @ c_HOL_Oone__class_Oone )
   != ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[1774:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(203,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).

thf(1000,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(405,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( E @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__le_0) ).

thf(1435,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( E @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(543,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).

thf(1726,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(371,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).

thf(1364,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(167,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(922,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(14648,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(paramod_ordered,[status(thm)],[8986,594]) ).

thf(14649,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(simp,[status(thm)],[14648]) ).

thf(14650,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[14649:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(394,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__div__algebra )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__inverse_0) ).

thf(1413,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__div__algebra )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(495,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_1) ).

thf(1626,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(16251,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(paramod_ordered,[status(thm)],[13895,560]) ).

thf(16252,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 ) ),
    inference(simp,[status(thm)],[16251]) ).

thf(16253,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[16252:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(177,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

thf(944,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(47,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

thf(663,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(522,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).

thf(1684,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(330,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oring__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).

thf(1277,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(264,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_9) ).

thf(1134,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(441,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__smult_0) ).

thf(1509,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(211,axiom,
    tc_RealDef_Oreal @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Oring__char__0) ).

thf(1018,plain,
    tc_RealDef_Oreal @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(87,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_9) ).

thf(754,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(189,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_1) ).

thf(968,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(297,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).

thf(1203,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(238,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).

thf(1081,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(6054,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield )
       != ( A @ class_Ring__and__Field_Ofield ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
    inference(paramod_ordered,[status(thm)],[1584,599]) ).

thf(6055,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield )
       != ( A @ class_Ring__and__Field_Ofield ) )
      | ( A @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div ) ),
    inference(simp,[status(thm)],[6054]) ).

thf(6056,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Divides_Osemiring__div,
    inference(pattern_uni,[status(thm)],[6055:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(85,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_9) ).

thf(749,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(6168,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[5450,574]) ).

thf(6169,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[6168]) ).

thf(6170,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[6169:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(423,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_3) ).

thf(1472,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(554,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).

thf(1748,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(58,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

thf(690,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(1906,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__ring__strict )
       != ( A @ class_Ring__and__Field_Oordered__ring__strict ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[953,1492]) ).

thf(1907,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__ring__strict )
       != ( A @ class_Ring__and__Field_Oordered__ring__strict ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1906]) ).

thf(1908,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[1907:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(1917,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[1908]) ).

thf(1935,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_RealDef_Oreal @ ( D @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(paramod_ordered,[status(thm)],[572,1917]) ).

thf(1936,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(pattern_uni,[status(thm)],[1935:[bind(A,$thf( tc_RealDef_Oreal )),bind(B,$thf( C )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).

thf(1943,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[1936]) ).

thf(1958,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1288,1943]) ).

thf(1959,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1958]) ).

thf(1961,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal != tc_Complex_Ocomplex )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1959]) ).

thf(151,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__0_0) ).

thf(887,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(485,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).

thf(1605,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(182,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).

thf(954,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(7552,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[6571,585]) ).

thf(7553,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[7552]) ).

thf(7554,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[7553:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(80,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Oinverse__divide_0) ).

thf(739,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(373,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).

thf(1368,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(1778,plain,
    ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) )
    | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
    | ~ $true
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
    inference(paramod_ordered,[status(thm)],[1772,557]) ).

thf(1779,plain,
    ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) )
    | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[1778]) ).

thf(1780,plain,
    ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
    inference(pattern_uni,[status(thm)],[1779:[]]) ).

thf(326,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).

thf(1267,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(1706,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(cnf,[status(esa)],[1705]) ).

thf(4317,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder )
       != ( B @ class_Orderings_Opreorder ) )
      | ~ ( B @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[590,1706]) ).

thf(4318,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder )
       != ( B @ class_Orderings_Opreorder ) )
      | ~ ( B @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[4317]) ).

thf(4319,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[4318:[bind(A,$thf( D )),bind(B,$thf( D @ tc_Polynomial_Opoly ))]]) ).

thf(4324,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[4319]) ).

thf(137,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_8) ).

thf(855,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(488,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_1) ).

thf(1611,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(275,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_2) ).

thf(1156,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(307,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).

thf(1225,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(551,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).

thf(1743,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(309,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).

thf(1230,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(428,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
        = B )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self2__is__id_0) ).

thf(1484,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
        = B )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(536,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_3) ).

thf(1711,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(51,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Int_Oring__char__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of_0) ).

thf(673,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Int_Oring__char__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(538,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).

thf(1716,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

thf(791,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(289,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).

thf(1186,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(8667,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[7581,585]) ).

thf(8668,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[8667]) ).

thf(8669,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[8668:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(16356,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_RealDef_Oreal @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(paramod_ordered,[status(thm)],[627,1917]) ).

thf(16357,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(pattern_uni,[status(thm)],[16356:[bind(A,$thf( tc_RealDef_Oreal )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).

thf(16374,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(simp,[status(thm)],[16357]) ).

thf(350,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).

thf(1317,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(241,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__by__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).

thf(1085,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__by__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(159,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_6) ).

thf(907,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(128,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_3) ).

thf(840,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(1776,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ $true
      | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
    inference(paramod_ordered,[status(thm)],[1772,1250]) ).

thf(1777,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[1776]) ).

thf(1783,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone )
       != A )
      | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != A )
      | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[1777]) ).

thf(1785,plain,
    ( ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Odivide ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
    | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
     != ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) ) ),
    inference(simp,[status(thm)],[1783]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).

thf(951,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_4) ).

thf(808,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
        = ( A @ ( C @ ( A @ ( C @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(334,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
        = C )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__mult__self1__is__id_0) ).

thf(1285,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Divides_Odiv__class_Odiv ) ) )
        = C )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(549,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).

thf(1738,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(358,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(1335,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(1336,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(cnf,[status(esa)],[1335]) ).

thf(38,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring) ).

thf(643,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(389,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_8) ).

thf(1404,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(82,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_1) ).

thf(744,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(456,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_1) ).

thf(1543,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(1847,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(paramod_ordered,[status(thm)],[909,569]) ).

thf(1848,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(simp,[status(thm)],[1847]) ).

thf(1849,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring,
    inference(pattern_uni,[status(thm)],[1848:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(64,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).

thf(703,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(268,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__inverse__le_0) ).

thf(1141,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(44,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1) ).

thf(656,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(532,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).

thf(1702,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(438,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).

thf(1504,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(139,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).

thf(859,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(314,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).

thf(1240,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(366,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).

thf(1353,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(226,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(1052,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(439,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).

thf(1506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(476,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_5) ).

thf(1585,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(246,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_6) ).

thf(1094,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(194,axiom,
    ( ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) )
    = ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

thf(978,plain,
    ( ( tc_Complex_Ocomplex @ ( v_w____ @ ( v_q____ @ c_Polynomial_Opoly ) ) )
    = ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( v_w____ @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(267,axiom,
    tc_Complex_Ocomplex @ class_Int_Onumber__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

thf(1140,plain,
    tc_Complex_Ocomplex @ class_Int_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(375,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).

thf(1372,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(328,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__divide_0) ).

thf(1272,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(8859,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[8230,592]) ).

thf(8860,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[8859]) ).

thf(8861,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[8860:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(4514,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[2187,585]) ).

thf(4515,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[4514]) ).

thf(4516,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[4515:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(146,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).

thf(876,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(131,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).

thf(845,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(397,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_0) ).

thf(1421,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ ( C @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(416,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(1459,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(286,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).

thf(1180,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(460,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).

thf(1553,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(193,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).

thf(976,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(508,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).

thf(1654,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(444,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).

thf(1517,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(90,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).

thf(759,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(1216,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(547,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__square_0) ).

thf(1734,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(252,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).

thf(1108,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(411,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Polynomial_Osmult ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Osmult ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_smult__smult_0) ).

thf(1448,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_Polynomial_Osmult ) ) @ ( B @ c_Polynomial_Osmult ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Polynomial_Osmult ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).

thf(1289,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(413,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).

thf(1453,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(479,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).

thf(1590,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(504,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).

thf(1646,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Omult__mono ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(2172,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[884,585]) ).

thf(2173,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[2172]) ).

thf(2174,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[2173:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(500,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_1) ).

thf(1639,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(42,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult) ).

thf(652,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(8720,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(paramod_ordered,[status(thm)],[909,614]) ).

thf(8721,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(simp,[status(thm)],[8720]) ).

thf(8722,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(pattern_uni,[status(thm)],[8721:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(447,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).

thf(1523,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(102,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).

thf(786,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Oone__class_Oone @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(100,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).

thf(781,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(201,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_1) ).

thf(995,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(587,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( G @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ~ ( A @ ( C @ ( F @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ( B = C )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(cnf,[status(esa)],[586]) ).

thf(588,plain,
    ! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( G @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ~ ( A @ ( C @ ( F @ ( E @ ( D @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield )
      | ( B = C ) ),
    inference(lifteq,[status(thm)],[587]) ).

thf(62,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).

thf(699,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(186,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__self_0) ).

thf(961,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(116,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).

thf(813,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(230,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

thf(1062,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Omult__zero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(163,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_6) ).

thf(914,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(8201,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[6930,585]) ).

thf(8202,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[8201]) ).

thf(8203,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[8202:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(5038,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[1796,592]) ).

thf(5039,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[5038]) ).

thf(5040,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[5039:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(236,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).

thf(1077,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(346,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).

thf(1309,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(409,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( E
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).

thf(1442,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( E
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
       != ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(4304,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    inference(paramod_ordered,[status(thm)],[909,590]) ).

thf(4305,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    inference(simp,[status(thm)],[4304]) ).

thf(4306,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Orderings_Opreorder,
    inference(pattern_uni,[status(thm)],[4305:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(223,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_5) ).

thf(1045,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(217,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_5) ).

thf(1030,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(293,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).

thf(1193,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(486,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(1607,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(92,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).

thf(763,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(155,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(899,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(512,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(1661,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( B = C )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(70,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).

thf(716,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(277,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).

thf(1161,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(489,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(1614,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(256,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).

thf(1116,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(364,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__fieldgb_Odivide__inverse_0) ).

thf(1348,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(502,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_4) ).

thf(1642,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(442,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).

thf(1512,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(472,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__1_0) ).

thf(1578,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(519,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_7) ).

thf(1678,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(8476,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[7067,574]) ).

thf(8477,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[8476]) ).

thf(8478,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[8477:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(125,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_0) ).

thf(833,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(457,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_negative__imp__inverse__negative_0) ).

thf(1546,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(494,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).

thf(1625,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(343,axiom,
    ! [A: $i] :
      ( ( tc_Complex_Ocomplex @ ( A @ ( v_q____ @ c_Polynomial_Opoly ) ) )
      = ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_qr_0) ).

thf(1303,plain,
    ! [A: $i] :
      ( ( tc_Complex_Ocomplex @ ( A @ ( v_q____ @ c_Polynomial_Opoly ) ) )
      = ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_q____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ ( v_q____ @ c_Polynomial_Opoly ) ) @ c_HOL_Oinverse__class_Oinverse ) @ c_Polynomial_Osmult ) ) @ c_Polynomial_Opoly ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(78,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).

thf(735,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(248,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).

thf(1097,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(126,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(835,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( B = C )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(449,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).

thf(1527,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(517,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).

thf(1673,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(510,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).

thf(1657,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(6486,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(paramod_ordered,[status(thm)],[5623,574]) ).

thf(6487,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero ) ),
    inference(simp,[status(thm)],[6486]) ).

thf(6488,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[6487:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(464,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__1__mult_0) ).

thf(1561,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(228,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__1_0) ).

thf(1056,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(16254,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[13895,592]) ).

thf(16255,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[16254]) ).

thf(16256,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[16255:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(231,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).

thf(1065,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( D @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(61,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(696,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(363,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).

thf(1346,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(170,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_9) ).

thf(928,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(165,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).

thf(918,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(110,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).

thf(801,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(4348,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[2160,585]) ).

thf(4349,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[4348]) ).

thf(4350,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[4349:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(434,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).

thf(1495,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( A @ c_HOL_Oone__class_Oone @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).

thf(1172,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(392,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).

thf(1410,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(94,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__self__if_0) ).

thf(767,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(16640,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[14407,585]) ).

thf(16641,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[16640]) ).

thf(16642,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[16641:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(35,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).

thf(635,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__idem__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(72,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).

thf(720,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(279,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).

thf(1165,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(623,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
        = D )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(cnf,[status(esa)],[622]) ).

thf(624,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( E @ ( D @ ( C @ ( B @ c_Polynomial_Opdivmod__rel ) ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield )
      | ( ( A @ tc_Polynomial_Opoly @ ( C @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
        = D ) ),
    inference(lifteq,[status(thm)],[623]) ).

thf(75,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).

thf(728,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Oone__class_Oone @ ( B @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(312,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).

thf(1236,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semiring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(262,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__one_0) ).

thf(1129,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Oone__class_Oone @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(273,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_3) ).

thf(1152,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(7582,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[6571,592]) ).

thf(7583,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[7582]) ).

thf(7584,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[7583:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(459,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_4) ).

thf(1550,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(368,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_5) ).

thf(1357,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(200,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).

thf(992,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).

thf(822,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(5044,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[2160,592]) ).

thf(5045,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[5044]) ).

thf(5046,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[5045:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_3) ).

thf(850,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(341,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_9) ).

thf(1299,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(6546,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[5663,585]) ).

thf(6547,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[6546]) ).

thf(6548,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[6547:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(258,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).

thf(1120,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(2136,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
       != ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1508,2133]) ).

thf(2137,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( ( A @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
       != ( A @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[2136]) ).

thf(2138,plain,
    ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Oone__class_Oone )
   != ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ c_HOL_Ozero__class_Ozero ) ),
    inference(pattern_uni,[status(thm)],[2137:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(380,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_1) ).

thf(1384,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(453,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_6) ).

thf(1537,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(474,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

thf(1582,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(212,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_0) ).

thf(1019,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(436,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).

thf(1500,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(73,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(723,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C = B )
      | ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(482,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).

thf(1597,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(403,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).

thf(1431,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__cancel__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(205,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_2) ).

thf(1004,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(4325,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Orderings_Opreorder )
       != ( A @ class_Orderings_Opreorder ) )
      | ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4306,579]) ).

thf(4326,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Orderings_Opreorder )
       != ( A @ class_Orderings_Opreorder ) )
      | ( A @ ( B @ ( B @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[4325]) ).

thf(4327,plain,
    ! [A: $i] : ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( A @ c_lessequals ) ) ),
    inference(pattern_uni,[status(thm)],[4326:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly )),bind(B,$thf( B ))]]) ).

thf(4345,plain,
    ! [A: $i] : ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( A @ c_lessequals ) ) ),
    inference(simp,[status(thm)],[4327]) ).

thf(144,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).

thf(871,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Oinverse ) )
        = ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(387,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).

thf(1399,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(492,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_9) ).

thf(1621,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(352,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).

thf(1320,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(175,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).

thf(940,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(288,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).

thf(1184,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(2057,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult ) ),
    inference(paramod_ordered,[status(thm)],[1508,565]) ).

thf(2058,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult ) ),
    inference(simp,[status(thm)],[2057]) ).

thf(2059,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult,
    inference(pattern_uni,[status(thm)],[2058:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(395,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_div__by__0_0) ).

thf(1416,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_Divides_Odiv__class_Odiv ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Divides_Osemiring__div ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(243,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).

thf(1088,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).

thf(1069,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(173,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__inverse_0) ).

thf(935,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Oinverse__class_Oinverse ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(207,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

thf(1009,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(418,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).

thf(1463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(466,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(1565,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_2) ).

thf(1037,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(97,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_7) ).

thf(775,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( A @ ( D @ c_Int_Onumber__class_Onumber__of ) @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(52,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).

thf(676,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(421,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_Complex_Ocomplex @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) )
      = ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__divide__def_0) ).

thf(1468,plain,
    ! [B: $i,A: $i] :
      ( ( tc_Complex_Ocomplex @ ( B @ ( A @ c_HOL_Oinverse__class_Odivide ) ) )
      = ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( B @ c_HOL_Oinverse__class_Oinverse ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(148,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_9) ).

thf(882,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ ( D @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(2175,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(paramod_ordered,[status(thm)],[1314,585]) ).

thf(2176,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(simp,[status(thm)],[2175]) ).

thf(2177,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Int_Onumber,
    inference(pattern_uni,[status(thm)],[2176:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(6931,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(paramod_ordered,[status(thm)],[5720,592]) ).

thf(6932,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__ring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(simp,[status(thm)],[6931]) ).

thf(6933,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[6932:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(209,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_2) ).

thf(1014,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Oordered__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(191,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ono__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).

thf(972,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(27900,plain,
    $false,
    inference(e,[status(thm)],[645,1411,1024,1190,1729,893,1315,1110,1686,1337,1718,1559,1105,909,628,9076,1083,777,555,666,1295,1200,683,730,5644,5000,1205,1269,1533,1437,861,582,762,2117,1406,614,1692,1305,597,1426,1671,1655,1137,797,5701,1260,2146,670,1497,1705,1867,2184,1275,2141,15916,1342,747,1222,930,829,898,7064,1441,709,1359,1386,1724,1265,5393,1127,1391,1576,973,885,1650,5723,565,1366,1623,1482,1254,1628,1709,570,1430,1330,751,802,1279,1455,1191,2126,949,1323,619,838,1059,1132,817,559,1379,1514,1247,1572,770,1398,5052,4771,17591,13895,638,853,1319,1890,1479,1609,1641,8703,1232,4253,1489,924,1465,1714,591,1040,1828,16693,574,905,5663,756,1664,1682,1136,806,7581,1581,966,692,1394,1351,660,988,1433,1600,602,5059,1169,687,1215,634,14372,6491,956,14410,866,1796,1072,1697,1242,2154,1521,1074,920,942,1691,793,4531,2164,8827,8397,7005,8481,1636,8233,5411,1470,6571,1067,1736,714,18112,1047,798,1163,5049,910,746,1021,1042,1519,1355,561,1487,1238,1570,1174,2133,598,16205,1502,820,788,1619,1370,815,5396,2132,13860,916,8920,879,1178,1457,583,1159,1210,1079,757,1195,1634,1291,1012,847,566,1032,1602,8700,625,852,1555,1740,842,1402,1360,1772,5006,1328,10731,1096,1006,1138,5373,593,610,1118,857,1592,742,578,1234,1541,874,1143,9073,615,1970,1227,980,1587,1567,1493,884,1361,1659,8017,1182,1461,5620,901,1424,1584,1700,4444,1644,1744,1419,1028,1082,1292,933,1016,1207,590,679,970,8230,706,622,1114,701,1297,1451,16690,2153,654,7485,1050,1720,779,605,1525,647,1263,997,1099,985,1150,1249,1530,1539,1382,1002,1852,569,1429,1333,633,1695,1563,1187,1616,953,718,926,1086,938,765,1054,5447,1035,1466,558,1026,1167,794,586,1278,1648,5666,1251,6053,1146,1680,1548,14303,1301,573,1219,824,4256,1747,1374,4365,1631,5043,733,5720,904,694,1389,772,13898,1652,579,1535,958,584,1154,14647,843,1125,826,577,711,1701,8581,1256,1488,1669,15919,572,1707,1271,1312,611,1733,1092,1090,804,947,1675,7482,641,1428,1258,8524,704,604,2119,831,1282,784,1574,1492,567,1722,2116,737,1690,1307,863,681,1408,1589,990,8986,649,616,1122,599,1376,1439,811,6165,631,1557,8983,621,848,1325,1344,668,1688,890,1667,1339,4445,1731,594,799,726,1149,964,983,1926,1474,1594,1213,1477,1102,658,18715,912,685,1198,1396,6574,959,2171,6907,1245,6930,1445,868,1176,608,1113,563,1775,1000,1435,1726,1364,1250,922,14650,1413,1626,16253,944,663,1684,1277,1134,1509,617,1018,754,968,5414,1203,589,1081,6056,749,6170,1472,1748,557,690,1961,887,1605,954,7554,739,1368,1780,1267,4324,580,855,1611,1156,1225,1743,1230,1484,2160,1711,673,1716,8858,791,1186,585,8669,16374,1317,1901,1085,907,17632,840,1785,951,808,1285,1738,5450,1336,643,1404,744,1543,1849,703,1141,656,1702,613,7067,1504,859,1240,1353,600,1052,1506,1585,1094,978,1140,1372,595,1272,612,8861,4516,876,845,1421,627,1459,1180,556,1553,976,581,1654,1517,759,1216,1734,1108,1448,2187,1289,1453,1590,1646,2174,896,1639,8584,652,632,8722,1523,786,781,995,588,699,961,813,1062,1508,568,914,8203,5040,1077,1212,1309,1442,4306,1045,1030,1491,1706,1193,1607,763,899,1661,716,1161,1614,1116,1348,620,1642,1512,1578,1678,8478,833,7666,1546,1625,1303,603,735,1097,835,1527,1148,1673,564,1314,1657,6488,1335,1561,1056,1288,16256,1065,696,1346,928,918,801,4350,1495,1172,1410,767,16642,635,720,1165,624,728,1236,1129,575,1152,7584,1550,1357,992,822,5623,5046,850,1299,5376,6548,1120,2138,1384,1537,1582,1019,1500,723,1597,1431,1004,4345,871,14407,1399,1621,1320,6173,940,1184,2059,1416,1088,1069,935,1009,1463,1565,1037,775,560,1917,676,592,1468,882,2177,6933,1014,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05  % Problem  : ALG400-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.12  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.50  % Computer : n014.cluster.edu
% 0.11/0.50  % Model    : x86_64 x86_64
% 0.11/0.50  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.50  % Memory   : 8046.5625MB
% 0.11/0.50  % OS       : Linux 6.8.0-71-generic
% 0.11/0.50  % CPULimit : 300
% 0.11/0.50  % WCLimit  : 300
% 0.11/0.50  % DateTime : Sat Sep 26 21:57:17 UTC 2026
% 0.11/0.50  % CPUTime  : 
% 0.11/0.50  Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.96/0.99  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 1.89/1.25  % [INFO] 	 Parsing done (253ms). 
% 1.89/1.25  % [INFO] 	 Running in sequential loop mode. 
% 2.78/1.46  % [INFO] 	 eprover registered as external prover. 
% 2.78/1.46  % [INFO] 	 Scanning for conjecture ... 
% 3.12/1.58  % [INFO] 	 Found a conjecture (or negated_conjecture) and 602 axioms. Running axiom selection ... 
% 4.07/1.70  % [INFO] 	 Axiom selection finished. Selected 552 axioms (removed 50 axioms). 
% 5.06/1.97  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 5.06/2.00  % [INFO] 	 Type checking passed. 
% 5.06/2.01  % [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 ... 
% 92.13/20.62  % External prover 'e' found a proof!
% 92.13/20.62  % [INFO] 	 Killing All external provers ... 
% 92.13/20.62  % Time passed: 19987ms (effective reasoning time: 19361ms)
% 92.13/20.63  % Axioms used in derivation (552): cls_divide__le__eq__number__of1_9, cls_divide__le__eq__number__of_9, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict, cls_divide__eq__eq_3, cls_le__divide__eq_3, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring, cls_order__le__less__trans_0, cls_less__divide__eq_3, cls_not__one__less__zero_0, cls_mult__less__cancel__left__disj_5, clsarity_Polynomial__Opoly__Ring__and__Field_Oidom, cls_le__divide__eq_8, cls_mult__zero__right_0, cls_zero__less__one_0, cls_divide__le__eq_2, cls_eq__divide__eq__number__of1_4, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_divide__less__0__iff_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_zero__less__divide__iff_5, cls_divide__eq__eq__number__of_4, cls_less__divide__eq__number__of1_6, cls_smult__smult_0, cls_divide__pos__pos_0, cls_mult__imp__le__div__pos_0, clsarity_RealDef__Oreal__Orderings_Opreorder, cls_mult__nonneg__nonneg_0, clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one, cls_mult__right__mono_0, cls_mult__right_Ozero_0, clsarity_Polynomial__Opoly__Orderings_Olinorder, cls_mult__less__cancel__right__disj_0, cls_divide__self_0, cls_mult__nonneg__nonpos2_0, cls_real__less__def_1, cls_negative__imp__inverse__negative_0, cls_pdivmod__rel__smult__right_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_divide__le__eq__number__of_4, cls_le__divide__eq__number__of1_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, cls_inverse__zero__imp__zero_0, cls_xt1_I12_J_0, clsarity_Complex__Ocomplex__Int_Onumber, cls_divide__nonpos__neg_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_mult__less__cancel__left__disj_1, cls_zero__le__one_0, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1, cls_inverse__eq__iff__eq_0, cls_zero__le__mult__iff_3, clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring, cls_divide__less__eq__number__of1_5, cls_CHAINED_0, cls_inverse__le__1__iff_2, cls_divide__le__eq__number__of1_4, cls_le__divide__eq__number__of_6, cls_zero__le__divide__iff_2, cls_linorder__neqE_0, cls_divide__1_0, cls_less__divide__eq__number__of_8, cls_nonzero__inverse__eq__divide_0, cls_divide__less__eq_4, cls_zero__less__divide__iff_0, cls_divide__le__eq_8, cls_less__divide__eq__number__of_3, cls_divide__less__eq__number__of1_0, cls_divide__less__eq__number__of_1, cls_less__imp__inverse__less__neg_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_le__divide__eq__number__of1_5, cls_divide__le__0__1__iff_1, cls_nonzero__norm__inverse_0, cls_divide__le__eq_7, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field, cls_mult__nonpos__nonneg_0, cls_inverse__less__1__iff_2, cls_one__le__inverse__iff_2, cls_inverse__1_0, cls_inverse__negative__iff__negative_1, clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring, cls_div__smult__right_0, cls_frac__le_0, cls_a00_0, cls_eq__divide__eq__number__of_4, cls_divide__eq__eq_0, cls_mult__nonpos__nonpos_0, cls_mult__less__imp__less__right_0, cls_left__inverse_0, cls_order__less__trans_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_divide__less__eq_5, cls_eq__divide__eq__number__of_1, cls_divide__less__eq__number__of1_6, cls_mult__le__cancel__left__pos_0, cls_split__mult__neg__le_0, cls_divide__le__0__iff_3, cls_mult__less__imp__less__left_0, cls_le__divide__eq__number__of1_9, cls_divide__le__eq__number__of_5, cls_less__divide__eq_4, cls_mult__less__cancel__right__disj_3, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono, cls_inverse__divide_0, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult, cls_mult__eq__0__iff_0, cls_divide__strict__left__mono_0, cls_inverse__nonnegative__iff__nonnegative_0, cls_div__by__0_0, cls_mult__less__cancel__left__disj_4, cls_lgqr_0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult, cls_frac__eq__eq_0, cls_divide__less__eq__number__of_6, cls_divide__eq__eq_4, cls_mult__left__mono__neg_0, cls_linorder__not__less_0, cls_less__divide__eq__number__of1_2, cls_mult_Ozero__left_0, cls_divide__neg__neg_0, cls_eq__divide__eq_4, cls_mult__mono_0, cls_class__semiring_Omul__0_0, cls_right__inverse__eq_0, cls_order__less__asym_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_inverse__le__1__iff_1, cls_less__divide__eq__number__of1_0, cls_order__le__less_0, cls_div__poly__eq_0, cls_divide__le__eq__number__of_8, cls_mult__strict__right__mono_0, cls_divide__less__eq__number__of1_8, clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors, cls_class__semiring_Omul__c_0, cls_mult__pos__neg_0, cls_div__mult__self2__is__id_0, cls_order__eq__refl_0, cls_zero__le__mult__iff_0, cls_le__divide__eq__number__of_7, cls_divide__eq__eq__number__of1_0, cls_inverse__eq__1__iff_1, cls_mult__strict__mono_0, clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero, cls_order__less__asym_H_0, clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__mult, clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra, cls_eq__number__of_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1, cls_mult_Ozero__right_0, cls_mult__left__mono_0, cls_divide__strict__left__mono__neg_0, cls_linorder__antisym__conv1_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero, cls_div__self_0, cls_linorder__antisym__conv2_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero, cls_div__mult__mult1_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom, cls_class__fieldgb_Oinverse__divide_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom, cls_norm__one_0, cls_class__semiring_Osemiring__rules_I12_J_0, cls_eq__divide__eq__number__of1_3, cls_divide__left__mono__neg_0, cls_inverse__nonzero__iff__nonzero_0, cls_less__divide__eq_7, cls_le__divide__eq_7, cls_inverse__nonpositive__iff__nonpositive_0, cls_inverse__nonnegative__iff__nonnegative_1, cls_divide__right__mono_0, cls_divide__right__mono__neg_0, cls_less__le__not__le_2, cls_divide__neg__pos_0, cls_divide__le__eq__number__of1_5, cls_xt1_I10_J_0, clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero, cls_less__divide__eq__number__of_7, cls_le__divide__eq_2, cls_divide__le__eq_3, cls_not__less__iff__gr__or__eq_0, cls_le__divide__eq__number__of_3, cls_divide__le__eq__number__of1_6, clsarity_RealDef__Oreal__Int_Onumber, cls_no__zero__divisors_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict, cls_mult__frac__num_0, cls_zero__le__mult__iff_4, cls_divide__less__eq_0, cls_divide__less__eq__number__of1_2, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_CHAINED_0_01, cls_mult__1__right_0, cls_divide__eq__eq__number__of_3, cls_less__divide__eq_2, cls_mult__le__0__iff_0, cls_le__divide__eq__number__of1_6, cls_mult__neg__pos_0, cls_zero__less__divide__iff_1, clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult, cls_mult__frac__frac_0, cls_divide__less__eq__number__of_0, cls_inverse__le__imp__le__neg_0, cls_mult__right__le__imp__le_0, cls_mult__pos__neg2_0, cls_divide__eq__eq__number__of1_3, cls_divide__less__eq__number__of1_7, cls_zero__le__divide__iff_3, cls_divide__le__eq__number__of_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring, cls_divide__le__eq__number__of_1, clsarity_RealDef__Oreal__Orderings_Olinorder, cls_class__semiring_Osemiring__rules_I15_J_0, cls_mult__mono1_0, cls_mult__less__cancel__left__disj_0, cls_le__imp__inverse__le_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1, cls_class__semiring_Osemiring__rules_I19_J_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra, cls_xt1_I8_J_0, cls_eq__divide__eq_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, cls_less__divide__eq__number__of_4, clsarity_Complex__Ocomplex__Int_Oring__char__0, cls_split__mult__pos__le_0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_mult__left__idem_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1, cls_mult__le__cancel__left__pos_1, cls_one__le__inverse__iff_1, cls_mult__le__cancel__left__neg_1, cls_less__divide__eq__number__of1_3, cls_zero__less__mult__pos_0, cls_divide__self__if_1, cls_mult__le__0__iff_1, cls_eq__divide__eq_3, cls_inverse__negative__imp__negative_0, cls_divide_Ozero_0, cls_divide__self__if_0, cls_le__divide__eq__number__of1_2, cls_class__semiring_Osemiring__rules_I17_J_0, clsarity_Polynomial__Opoly__Divides_Osemiring__div, cls_mult__imp__div__pos__le_0, cls_mult__le__0__iff_4, clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict, clsarity_RealDef__Oreal__Int_Oring__char__0, cls_smult__1__left_0, cls_eq__divide__eq__number__of_3, cls_zero__le__divide__iff_5, cls_divide__less__0__iff_3, cls_linorder__linear_0, clsarity_Polynomial__Opoly__Int_Onumber, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1, cls_not__leE_0, cls_divide__less__eq_8, cls_mult__less__cancel__right__disj_2, cls_qr_0, cls_order__trans_0, cls_divide__nonneg__neg_0, cls_less__divide__eq__number__of1_7, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, cls_mult__strict__left__mono_0, cls_divide__le__0__iff_2, cls_le__number__of__eq__not__less_1, cls_divide__eq__eq__number__of_0, cls_divide__less__eq__number__of_7, cls_order__antisym_0, cls_divide__le__eq_6, cls_divide__less__eq_1, cls_less__divide__eq__number__of_0, cls_mult__left__less__imp__less_0, cls_linorder__antisym__conv1_1, cls_no__zero__divirors__neq0_0, cls_inverse__nonzero__iff__nonzero_1, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict, cls_div__by__1_0, cls_inverse__le__1__iff_0, cls_mult__le__0__iff_5, cls_divide__le__eq__number__of1_2, cls_mult__strict__mono_H_0, cls_zero__neq__one_0, cls_zero__le__divide__iff_4, cls_inverse__eq__1__iff_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one, cls_less__divide__eq_5, cls_split__mult__pos__le_1, cls_le__divide__eq__number__of_2, cls_less__divide__eq_8, cls_divide__le__eq_0, cls_zero__less__divide__iff_3, cls_le__divide__eq__number__of_8, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring, cls_less__1__mult_0, cls_divide__less__eq__number__of1_9, cls_less__imp__inverse__less_0, clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult, cls_divide__nonneg__pos_0, cls_divide__zero_0, cls_divide__less__eq__number__of_4, cls_mult__less__cancel__right__disj_5, clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one, cls_inverse__less__1__iff_0, cls_divide__le__0__iff_5, cls_linorder__not__le_1, cls_divide__le__eq_4, cls_class__semiring_Omul__a_0, cls_not__less__iff__gr__or__eq_1, cls_zero__le__square_0, cls_inverse__positive__iff__positive_0, cls_class__semiring_Omul__1_0, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero, cls_inverse__positive__iff__positive_1, clsarity_Complex__Ocomplex__Ring__and__Field_Oidom, cls_eq__divide__eq__number__of1_2, cls_right__inverse_0, cls_order__le__neq__trans_0, cls_divide__less__eq__number__of1_3, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring, cls_mult__nonneg__nonpos_0, cls_less__divide__eq_1, cls_zero__less__divide__iff_2, cls_inverse__unique_0, cls_order__eq__iff_2, clsarity_RealDef__Oreal__Ring__and__Field_Oidom, cls_le__divide__eq_6, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1, cls_mult__left__le__one__le_0, cls_less__le__not__le_1, cls_le__divide__eq__number__of_1, cls_le__divide__eq_1, cls_divide__le__0__iff_1, cls_divide__le__eq__number__of1_7, cls_not__square__less__zero_0, cls_less__divide__eq__number__of_1, cls_linorder__antisym__conv3_0, cls_mult__imp__less__div__pos_0, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono, cls_le__divide__eq_0, cls_divide__zero__left_0, cls_linorder__neqE__ordered__idom_0, cls_divide__pos__neg_0, cls_one__less__inverse__iff_2, cls_one__le__inverse__iff_0, cls_mult__eq__0__iff_2, cls_eq__divide__eq_2, cls_order__neq__le__trans_0, cls_divide__eq__eq__number__of_1, cls_mult__strict__left__mono__comm_0, cls_norm__inverse_0, cls_less__divide__eq__number__of_6, cls_mult__less__cancel__left__neg_1, cls_order__antisym__conv_0, cls_less__divide__eq__number__of1_8, cls_mult__mono_H_0, cls_complex__divide__def_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_divide__less__eq_2, cls_divide__less__0__1__iff_0, cls_divide__le__eq__number__of_7, cls_linorder__less__linear_0, cls_inverse__negative__iff__negative_0, cls_nonzero__inverse__inverse__eq_0, cls_div__0_0, cls_divide__le__eq__number__of_2, clsarity_RealDef__Oreal__Ring__and__Field_Ofield, cls_order__less__le_2, cls_divide__strict__right__mono__neg_0, cls_mult__less__cancel__left__pos_1, cls_le__divide__eq__number__of_5, cls_le__divide__eq__number__of1_7, cls_zero__le__mult__iff_5, cls_divide__le__eq_5, clsarity_Polynomial__Opoly__Int_Oring__char__0, cls_eq__divide__imp_0, cls_class__semiring_Osemiring__rules_I11_J_0, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0, cls_eq__divide__eq__number__of_2, clsarity_RealDef__Oreal__RealVector_Oreal__normed__field, cls_inverse__eq__divide__number__of_0, cls_nonzero__inverse__eq__imp__eq_0, cls_zero__le__mult__iff_1, cls_pdivmod__rel__smult__left_0, cls_divide__eq__imp_0, cls_divide__less__eq__number__of_8, cls_divide__eq__eq__number__of1_4, cls_xt1_I11_J_0, cls_zero__le__divide__iff_0, cls_mult__imp__div__pos__less_0, cls_one__neq__zero_0, cls_mult__le__cancel__left__neg_0, cls_divide__less__eq_7, cls_less__divide__eq__number__of1_4, cls_mult__le__0__iff_2, cls_divide__less__0__iff_5, cls_class__semiring_Osemiring__rules_I18_J_0, cls_mult__right__le__one__le_0, cls_divide__less__eq__number__of_3, cls_mult__right__mono__neg_0, cls_le__divide__eq__number__of1_3, cls_divide__less__0__iff_2, cls_xt1_I6_J_0, cls_positive__imp__inverse__positive_0, cls_inverse__inverse__eq_0, cls_divide__left__mono_0, cls_mult__1_0, cls_mult__less__cancel__left__disj_3, cls_divide__le__eq__number__of1_1, cls_zero__less__mult__pos2_0, cls_divide__eq__eq__number__of1_1, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0, cls_mult__less__cancel__right__disj_4, cls_mult__1__left_0, cls_one__less__inverse__iff_0, cls_mult__zero__left_0, cls_frac__eq__eq_1, cls_divide__le__0__iff_4, clsarity_Polynomial__Opoly__Int_Onumber__ring, cls_linorder__not__le_0, cls_div__mult__mult2_0, cls_le__divide__eq_9, cls_poly__smult_0, cls_zero__less__divide__1__iff_1, cls_inverse__less__1__iff_1, cls_zero__le__divide__1__iff_1, clsarity_Polynomial__Opoly__Orderings_Oorder, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult, cls_frac__less2_0, cls_divide__less__eq__number__of_9, cls_le__divide__eq_4, cls_less__divide__eq_6, cls_divide__le__eq__number__of1_8, cls_mult__pos__pos_0, cls_mult__left__le__imp__le_0, cls_mult__strict__right__mono__neg_0, clsarity_Polynomial__Opoly__Orderings_Opreorder, cls_class__fieldgb_Odivide__inverse_0, cls_divide__less__0__iff_1, cls_order__less__irrefl_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field, cls_divide__le__eq__number__of1_3, cls_one__less__inverse__iff_1, cls_divide__less__eq__number__of1_4, cls_inverse__less__imp__less__neg_0, cls_zero__less__divide__iff_4, cls_inverse__eq__divide_0, cls_divide__le__0__iff_0, cls_mult__right__less__imp__less_0, cls_pdivmod__rel__unique_1, cls_less__divide__eq__number__of_2, cls_inverse__le__imp__le_0, cls_divide__less__eq_9, cls_inverse__zero_0, cls_le__divide__eq__number__of1_1, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom, cls_eq__divide__eq__number__of1_0, cls_mult__divide__mult__cancel__right_0, cls_mult__less__cancel__left__disj_2, cls_frac__less_0, cls_r01_0, cls_mult__less__cancel__right__disj_1, cls_divide__le__eq_9, clsarity_RealDef__Oreal__Orderings_Oorder, cls_divide__strict__right__mono_0, clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult, cls_divide__inverse_0, cls_field__inverse_0, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring, cls_divide__less__eq_6, cls_pdivmod__rel__unique_0, cls_less__divide__eq__number__of1_9, cls_divide__eq__eq__number__of_2, cls_inverse__mult__distrib_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring, cls_eq__divide__eq__number__of_0, cls_mult__eq__0__iff_1, cls_divide__nonpos__pos_0, cls_less__divide__eq_0, cls_divide__less__eq__number__of_2, cls_inverse__positive__imp__positive_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom, cls_divide__less__eq_3, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, cls_nonzero__inverse__mult__distrib_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring, cls_inverse__less__imp__less_0, cls_order__less__imp__le_0, cls_le__divide__eq__number__of1_4, cls_div__mult__self1__is__id_0, cls_mult__idem_0, cls_le__imp__inverse__le__neg_0, cls_less__divide__eq__number__of_5, cls_le__divide__eq__number__of_4, cls_zero__le__divide__iff_1, cls_div__mult__mult1__if_0, cls_divide__less__eq__number__of1_1, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring, cls_divide__le__eq__number__of1_0, clsarity_RealDef__Oreal__Int_Onumber__ring, cls_div__smult__left_0, cls_divide__eq__eq_1, cls_le__divide__eq_5, clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict, cls_zero__less__divide__1__iff_0, cls_xt1_I7_J_0, cls_inverse__nonpositive__iff__nonpositive_1, cls_not__one__le__zero_0, cls_mult__less__le__imp__less_0, cls_mult__divide__mult__cancel__left_0, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, cls_divide__less__0__1__iff_1, cls_le__divide__eq__number__of1_8, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1, cls_divide__less__eq__number__of_5, cls_order__less__le_1, cls_mult__le__0__iff_3, cls_mult__neg__neg_0, cls_linorder__not__less_1, cls_mult__less__cancel__left__neg_0, clsarity_Complex__Ocomplex__Int_Onumber__ring, cls_less__divide__eq__number__of1_5, clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors, cls_zero__le__divide__1__iff_0, cls_less__divide__eq_9, cls_divide__le__eq__number__of_3, cls_le__divide__eq__number__of_9, cls_less__divide__eq__number__of_9, cls_le__divide__eq__number__of_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, cls_mult__less__cancel__left__pos_0, cls_divide__less__0__iff_4, cls_split__mult__neg__le_1, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors, cls_zero__le__mult__iff_2, cls_divide__le__eq_1, cls_divide__le__0__1__iff_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__strict__left__mono__neg_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict, cls_le__number__of__eq__not__less_0, cls_right__inverse__eq_1, cls_divide__le__eq__number__of_6, cls_less__divide__eq__number__of1_1
% 92.13/20.63  % No. of inferences in proof: 1613
% 92.13/20.63  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19987 ms resp. 19361 ms w/o parsing
% 95.20/21.03  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 95.20/21.04  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------