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

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%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ALG342-1 : 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 06:46:40 AM UTC 2026

% Result   : Unsatisfiable 104.09s 24.66s
% Output   : Refutation 108.32s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   43
%            Number of leaves      :  565
% Syntax   : Number of formulae    : 1862 ( 385 unt;   0 typ;   0 def)
%            Number of atoms       : 5834 ( 906 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives : 23589 (3130   ~;3136   |;   0   &;17323   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   18 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   83 (  80 usr;   8 con; 0-3 aty)
%            Number of variables   : 3690 (   0   ^;3690   !;   0   ?;3690   :)

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

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

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

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

thf(v_r_decl,type,
    v_r: $i ).

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

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

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

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

thf(c_Polynomial_OpCons_decl,type,
    c_Polynomial_OpCons: $i > $i > $i > $i ).

thf(v_c_____decl,type,
    v_c____: $i ).

thf(v_cs_____decl,type,
    v_cs____: $i ).

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

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

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

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

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

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

thf(class_OrderedGroup_Ocancel__comm__monoid__add_decl,type,
    class_OrderedGroup_Ocancel__comm__monoid__add: $i > $o ).

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

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

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

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

thf(class_Ring__and__Field_Oring__1__no__zero__divisors_decl,type,
    class_Ring__and__Field_Oring__1__no__zero__divisors: $i > $o ).

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

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

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

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

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

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

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

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

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

thf(class_Ring__and__Field_Osgn__if_decl,type,
    class_Ring__and__Field_Osgn__if: $i > $o ).

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

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

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

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

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

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

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

thf(c_HOL_Osgn__class_Osgn_decl,type,
    c_HOL_Osgn__class_Osgn: $i > $i > $i ).

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_Ocomm__semiring_decl,type,
    class_Ring__and__Field_Ocomm__semiring: $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_RealVector_Oreal__normed__div__algebra_decl,type,
    class_RealVector_Oreal__normed__div__algebra: $i > $o ).

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

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_Ring__and__Field_Osemiring_decl,type,
    class_Ring__and__Field_Osemiring: $i > $o ).

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

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

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

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

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

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

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

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

thf(c_Transcendental_Oln_decl,type,
    c_Transcendental_Oln: $i > $i ).

thf(c_Polynomial_Opos__poly_decl,type,
    c_Polynomial_Opos__poly: $i > $i > $o ).

thf(c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1_decl,type,
    c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1: $i > $i > $i ).

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

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

thf(v_sko__local__XpCons__1_decl,type,
    v_sko__local__XpCons__1: $i > $i > $i ).

thf(c_RealDef_Oreal__of__preal_decl,type,
    c_RealDef_Oreal__of__preal: $i > $i ).

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

thf(c_HOL_Oabs__class_Oabs_decl,type,
    c_HOL_Oabs__class_Oabs: $i > $i > $i ).

thf(v_m_____decl,type,
    v_m____: $i ).

thf(v_sko__local__XpCons__Xhyps__1_decl,type,
    v_sko__local__XpCons__Xhyps__1: $i > $i > $i ).

thf(96,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__semigroup__add) ).

thf(809,plain,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(539,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__comm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add) ).

thf(1711,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(11,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add) ).

thf(586,plain,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(587,plain,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(cnf,[status(esa)],[586]) ).

thf(1916,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[1711,587]) ).

thf(1917,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(simp,[status(thm)],[1916]) ).

thf(1918,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add,
    inference(pattern_uni,[status(thm)],[1917:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(2092,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[1918,587]) ).

thf(2093,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(simp,[status(thm)],[2092]) ).

thf(2094,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add,
    inference(pattern_uni,[status(thm)],[2093:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(28,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

thf(629,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(418,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(1469,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)],[418]) ).

thf(354,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(1343,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(4,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(572,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)],[4]) ).

thf(573,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[572]) ).

thf(1823,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_Ocomm__semiring__1 ) ),
    inference(paramod_ordered,[status(thm)],[1343,573]) ).

thf(1824,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_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[1823]) ).

thf(1825,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(pattern_uni,[status(thm)],[1824:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(1993,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(paramod_ordered,[status(thm)],[1825,573]) ).

thf(1994,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[1993]) ).

thf(1995,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(pattern_uni,[status(thm)],[1994:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(239,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).

thf(1105,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(548,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__assoc_0) ).

thf(1729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(27,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(627,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)],[27]) ).

thf(628,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(cnf,[status(esa)],[627]) ).

thf(505,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

thf(1644,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(10,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(584,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)],[10]) ).

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

thf(1902,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(paramod_ordered,[status(thm)],[1644,585]) ).

thf(1903,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(simp,[status(thm)],[1902]) ).

thf(1904,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom,
    inference(pattern_uni,[status(thm)],[1903:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(2089,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(paramod_ordered,[status(thm)],[1904,585]) ).

thf(2090,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(simp,[status(thm)],[2089]) ).

thf(2091,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom,
    inference(pattern_uni,[status(thm)],[2090:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(2338,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(paramod_ordered,[status(thm)],[2091,585]) ).

thf(2339,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(simp,[status(thm)],[2338]) ).

thf(2340,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom,
    inference(pattern_uni,[status(thm)],[2339:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2785,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(paramod_ordered,[status(thm)],[2340,585]) ).

thf(2786,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(simp,[status(thm)],[2785]) ).

thf(2787,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom,
    inference(pattern_uni,[status(thm)],[2786:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2170,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(paramod_ordered,[status(thm)],[1995,573]) ).

thf(2171,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[2170]) ).

thf(2172,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(pattern_uni,[status(thm)],[2171:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(12,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(588,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)],[12]) ).

thf(589,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult ) ),
    inference(cnf,[status(esa)],[588]) ).

thf(2542,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2172,589]) ).

thf(2543,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2542]) ).

thf(2544,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult,
    inference(pattern_uni,[status(thm)],[2543:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(273,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).

thf(1179,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(304,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).

thf(1238,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(8,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add) ).

thf(580,plain,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

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

thf(1816,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[1238,581]) ).

thf(1817,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(simp,[status(thm)],[1816]) ).

thf(1818,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add,
    inference(pattern_uni,[status(thm)],[1817:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(460,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(1549,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)],[460]) ).

thf(241,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).

thf(1110,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Power_Opower )
      | ~ ( A @ class_Ring__and__Field_Omult__zero )
      | ~ ( A @ class_Ring__and__Field_Ono__zero__divisors )
      | ~ ( A @ class_Ring__and__Field_Ozero__neq__one ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(34,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(644,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)],[34]) ).

thf(645,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)],[644]) ).

thf(134,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(892,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)],[134]) ).

thf(458,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(1546,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(1889,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_Ocomm__semiring__1 ) ),
    inference(paramod_ordered,[status(thm)],[1546,573]) ).

thf(1890,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_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[1889]) ).

thf(1891,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(pattern_uni,[status(thm)],[1890:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(2047,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(paramod_ordered,[status(thm)],[1891,573]) ).

thf(2048,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[2047]) ).

thf(2049,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(pattern_uni,[status(thm)],[2048:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(3019,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(paramod_ordered,[status(thm)],[2049,628]) ).

thf(3020,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(simp,[status(thm)],[3019]) ).

thf(3021,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(pattern_uni,[status(thm)],[3020:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(344,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_0) ).

thf(1322,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(206,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(1041,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(9,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(582,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)],[9]) ).

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

thf(1835,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__idom ) ),
    inference(paramod_ordered,[status(thm)],[1041,583]) ).

thf(1836,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__idom ) ),
    inference(simp,[status(thm)],[1835]) ).

thf(1837,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom,
    inference(pattern_uni,[status(thm)],[1836:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(2019,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[1837,583]) ).

thf(2020,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2019]) ).

thf(2021,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom,
    inference(pattern_uni,[status(thm)],[2020:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(2204,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[2021,583]) ).

thf(2205,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2204]) ).

thf(2206,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom,
    inference(pattern_uni,[status(thm)],[2205:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(36,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(649,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)],[36]) ).

thf(650,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(cnf,[status(esa)],[649]) ).

thf(4445,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2206,650]) ).

thf(4446,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[4445]) ).

thf(4447,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom,
    inference(pattern_uni,[status(thm)],[4446:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(543,axiom,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( v_m____ @ ( v_r @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( v_c____ @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_cs____ @ ( v_c____ @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(1718,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( v_m____ @ ( v_r @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( v_c____ @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( tc_Complex_Ocomplex @ ( v_cs____ @ ( v_c____ @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(369,axiom,
    tc_RealDef_Oreal @ class_Int_Onumber__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).

thf(1369,plain,
    tc_RealDef_Oreal @ class_Int_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(280,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(1190,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)],[280]) ).

thf(268,axiom,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( A @ c_RealDef_Oreal__of__preal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__gt__zero__preal__Ex_1) ).

thf(1168,plain,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( A @ c_RealDef_Oreal__of__preal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(237,axiom,
    tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons_0) ).

thf(1101,plain,
    tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(1,negated_conjecture,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(566,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(568,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(cnf,[status(esa)],[566]) ).

thf(3865,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ $true
      | ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1101,568]) ).

thf(3866,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
      | ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[3865]) ).

thf(3867,plain,
    tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ),
    inference(pattern_uni,[status(thm)],[3866:[bind(A,$thf( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) ))]]) ).

thf(414,axiom,
    tc_RealDef_Oreal @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).

thf(1463,plain,
    tc_RealDef_Oreal @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(165,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(952,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)],[165]) ).

thf(953,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(cnf,[status(esa)],[952]) ).

thf(1852,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Orderings_Olinorder )
       != ( A @ class_Orderings_Olinorder ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1463,953]) ).

thf(1853,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Orderings_Olinorder )
       != ( A @ class_Orderings_Olinorder ) )
      | ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1852]) ).

thf(1854,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(pattern_uni,[status(thm)],[1853:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(1864,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1854]) ).

thf(3978,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) ) )
      | ~ $true
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(paramod_ordered,[status(thm)],[3867,1864]) ).

thf(3979,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[3978]) ).

thf(3980,plain,
    ~ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ ( v_r @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[3979:[bind(A,$thf( v_r )),bind(B,$thf( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) ))]]) ).

thf(4002,plain,
    ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ ( v_r @ c_HOL_Oord__class_Oless ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1101,3980]) ).

thf(4003,plain,
    ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
   != ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ ( v_r @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[4002]) ).

thf(4004,plain,
    ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
    | ( ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) )
     != ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) ) )
    | ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )
     != v_r ) ),
    inference(simp,[status(thm)],[4003]) ).

thf(4005,plain,
    ( ( ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) )
     != ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) ) )
    | ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )
     != v_r ) ),
    inference(simp,[status(thm)],[4004]) ).

thf(142,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(907,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(7,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(578,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)],[7]) ).

thf(579,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)],[578]) ).

thf(1801,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)],[907,579]) ).

thf(1802,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)],[1801]) ).

thf(1803,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[1802:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(1987,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)],[1803,579]) ).

thf(1988,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)],[1987]) ).

thf(1989,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[1988:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(20,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(607,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)],[20]) ).

thf(608,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)],[607]) ).

thf(2334,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)],[1989,608]) ).

thf(2335,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)],[2334]) ).

thf(2336,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[2335:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(195,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).

thf(1020,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

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

thf(570,plain,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Oab__group__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(571,plain,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Oab__group__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(cnf,[status(esa)],[570]) ).

thf(1773,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(paramod_ordered,[status(thm)],[1020,571]) ).

thf(1774,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(simp,[status(thm)],[1773]) ).

thf(1775,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add,
    inference(pattern_uni,[status(thm)],[1774:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(1971,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(paramod_ordered,[status(thm)],[1775,571]) ).

thf(1972,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(simp,[status(thm)],[1971]) ).

thf(1973,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add,
    inference(pattern_uni,[status(thm)],[1972:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(2129,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(paramod_ordered,[status(thm)],[1973,571]) ).

thf(2130,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(simp,[status(thm)],[2129]) ).

thf(2131,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add,
    inference(pattern_uni,[status(thm)],[2130:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2478,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(paramod_ordered,[status(thm)],[2131,571]) ).

thf(2479,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(simp,[status(thm)],[2478]) ).

thf(2480,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add,
    inference(pattern_uni,[status(thm)],[2479:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(228,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

thf(1083,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(13,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(590,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)],[13]) ).

thf(591,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
    inference(cnf,[status(esa)],[590]) ).

thf(298,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(1226,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)],[298]) ).

thf(1227,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(cnf,[status(esa)],[1226]) ).

thf(1928,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder )
       != ( B @ class_Orderings_Oorder ) )
      | ~ ( B @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[591,1227]) ).

thf(1929,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder )
       != ( B @ class_Orderings_Oorder ) )
      | ~ ( B @ ( C @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[1928]) ).

thf(1930,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[1929:[bind(A,$thf( D )),bind(B,$thf( D @ tc_Polynomial_Opoly ))]]) ).

thf(1933,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)],[1930]) ).

thf(1980,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1041,1933]) ).

thf(1981,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1980]) ).

thf(1982,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[1981:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal ))]]) ).

thf(66,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C = E )
      | ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).

thf(730,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C = E )
      | ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(405,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(1443,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)],[405]) ).

thf(493,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) )
       != ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).

thf(1618,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) )
       != ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(184,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(994,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)],[184]) ).

thf(384,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_0) ).

thf(1401,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(457,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).

thf(1544,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(479,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(1591,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)],[479]) ).

thf(427,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(1486,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)],[427]) ).

thf(559,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(1750,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)],[559]) ).

thf(177,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__0__left_0) ).

thf(977,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(264,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( 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__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_0) ).

thf(1158,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( 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__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(386,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(1406,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)],[386]) ).

thf(1983,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[583,1933]) ).

thf(1984,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[1983]) ).

thf(1985,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[1984:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ tc_Polynomial_Opoly ))]]) ).

thf(1986,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[1985]) ).

thf(2034,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[583,1986]) ).

thf(2035,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2034]) ).

thf(2036,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[2035:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ tc_Polynomial_Opoly ))]]) ).

thf(2040,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2036]) ).

thf(2098,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[583,2040]) ).

thf(2099,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2098]) ).

thf(2100,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[2099:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ tc_Polynomial_Opoly ))]]) ).

thf(2104,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2100]) ).

thf(70,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = E )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

thf(741,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = E )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(223,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(1073,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)],[223]) ).

thf(126,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(878,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)],[126]) ).

thf(38,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(654,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)],[38]) ).

thf(655,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    inference(cnf,[status(esa)],[654]) ).

thf(22,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

thf(612,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(613,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(cnf,[status(esa)],[612]) ).

thf(614,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add )
      | ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(lifteq,[status(thm)],[613]) ).

thf(529,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ratiotest__lemma_0) ).

thf(1692,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( D @ c_RealVector_Onorm__class_Onorm ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(336,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(1305,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(16,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(597,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)],[16]) ).

thf(535,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(1705,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)],[535]) ).

thf(488,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mono_0) ).

thf(1608,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_Power_Opower__class_Opower ) ) @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(511,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn0_0) ).

thf(1655,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Osgn__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(254,axiom,
    tc_Complex_Ocomplex @ class_HOL_Ozero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__HOL_Ozero) ).

thf(1137,plain,
    tc_Complex_Ocomplex @ class_HOL_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

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

thf(642,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(643,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(cnf,[status(esa)],[642]) ).

thf(4009,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(paramod_ordered,[status(thm)],[1837,643]) ).

thf(4010,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(simp,[status(thm)],[4009]) ).

thf(4011,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(pattern_uni,[status(thm)],[4010:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(552,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(1735,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)],[552]) ).

thf(130,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).

thf(884,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(1865,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(paramod_ordered,[status(thm)],[884,585]) ).

thf(1866,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(simp,[status(thm)],[1865]) ).

thf(1867,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom,
    inference(pattern_uni,[status(thm)],[1866:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(91,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(797,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)],[91]) ).

thf(98,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

thf(814,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( E @ ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(503,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

thf(1640,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(218,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(1063,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__ring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(4433,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ 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)],[1837,650]) ).

thf(4434,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ 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)],[4433]) ).

thf(4435,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom,
    inference(pattern_uni,[status(thm)],[4434:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(360,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__linear_0) ).

thf(1354,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(44,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(670,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)],[44]) ).

thf(2138,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[583,2104]) ).

thf(2139,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2138]) ).

thf(2140,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[2139:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ tc_Polynomial_Opoly ))]]) ).

thf(2144,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2140]) ).

thf(2474,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2021,2144]) ).

thf(2475,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2474]) ).

thf(2476,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[2475:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(54,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(698,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)],[54]) ).

thf(565,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(1761,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(72,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_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).

thf(747,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_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(437,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(1507,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)],[437]) ).

thf(154,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(930,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(104,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(829,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)],[104]) ).

thf(283,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(1196,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)],[283]) ).

thf(4790,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2206,655]) ).

thf(4791,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    inference(simp,[status(thm)],[4790]) ).

thf(4792,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Orderings_Opreorder,
    inference(pattern_uni,[status(thm)],[4791:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(261,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__comm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add) ).

thf(1152,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(1885,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[1152,587]) ).

thf(1886,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(simp,[status(thm)],[1885]) ).

thf(1887,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add,
    inference(pattern_uni,[status(thm)],[1886:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(2044,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[1887,587]) ).

thf(2045,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(simp,[status(thm)],[2044]) ).

thf(2046,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add,
    inference(pattern_uni,[status(thm)],[2045:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(109,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Oln @ ( A @ c_Transcendental_Oln @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ln__less__cancel__iff_1) ).

thf(841,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Oln @ ( A @ c_Transcendental_Oln @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(490,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).

thf(1613,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(363,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(1360,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(39,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(656,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)],[39]) ).

thf(657,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(cnf,[status(esa)],[656]) ).

thf(4914,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)],[1360,657]) ).

thf(4915,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)],[4914]) ).

thf(4916,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[4915:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

thf(651,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(307,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(1243,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)],[307]) ).

thf(199,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(1027,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(5,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(574,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)],[5]) ).

thf(575,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)],[574]) ).

thf(1780,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)],[1027,575]) ).

thf(1781,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)],[1780]) ).

thf(1782,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[1781:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(2471,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[583,2144]) ).

thf(2472,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2471]) ).

thf(2473,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[2472:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ tc_Polynomial_Opoly ))]]) ).

thf(2477,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2473]) ).

thf(2642,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[583,2477]) ).

thf(2643,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2642]) ).

thf(2644,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[2643:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ tc_Polynomial_Opoly ))]]) ).

thf(2651,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2644]) ).

thf(2772,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[583,2651]) ).

thf(2773,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2772]) ).

thf(2774,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[2773:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ tc_Polynomial_Opoly ))]]) ).

thf(2781,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2774]) ).

thf(3237,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[583,2781]) ).

thf(3238,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[3237]) ).

thf(3239,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[3238:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ tc_Polynomial_Opoly ))]]) ).

thf(3249,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ 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 @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[3239]) ).

thf(403,axiom,
    tc_RealDef_Oreal @ class_HOL_Ozero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__HOL_Ozero) ).

thf(1441,plain,
    tc_RealDef_Oreal @ class_HOL_Ozero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(175,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__right__cancel_0) ).

thf(973,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A = C )
      | ( B
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(131,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(885,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)],[131]) ).

thf(506,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

thf(1645,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(1919,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)],[1041,591]) ).

thf(1920,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)],[1919]) ).

thf(1921,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Orderings_Oorder,
    inference(pattern_uni,[status(thm)],[1920:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(484,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(1601,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)],[484]) ).

thf(378,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(1386,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)],[378]) ).

thf(443,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(1517,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)],[443]) ).

thf(1518,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(cnf,[status(esa)],[1517]) ).

thf(534,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(1703,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)],[534]) ).

thf(299,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

thf(1228,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(495,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(1623,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)],[495]) ).

thf(313,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(1254,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)],[313]) ).

thf(420,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(1473,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(1872,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)],[1473,579]) ).

thf(1873,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)],[1872]) ).

thf(1874,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[1873:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(2041,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)],[1874,579]) ).

thf(2042,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)],[2041]) ).

thf(2043,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(pattern_uni,[status(thm)],[2042:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(2288,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)],[2043,579]) ).

thf(2289,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)],[2288]) ).

thf(2290,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)],[2289:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2652,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)],[2290,579]) ).

thf(2653,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)],[2652]) ).

thf(2654,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)],[2653:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(537,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(1709,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Odivision__by__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(2037,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1837,1986]) ).

thf(2038,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2037]) ).

thf(2039,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[2038:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

thf(719,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(93,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(802,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(340,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( D = E )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).

thf(1313,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( D = E )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(4021,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(paramod_ordered,[status(thm)],[2206,643]) ).

thf(4022,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(simp,[status(thm)],[4021]) ).

thf(4023,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(pattern_uni,[status(thm)],[4022:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(1990,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[1818,581]) ).

thf(1991,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(simp,[status(thm)],[1990]) ).

thf(1992,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add,
    inference(pattern_uni,[status(thm)],[1991:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(216,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(1059,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)],[216]) ).

thf(513,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

thf(1660,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(333,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(1298,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)],[333]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osgn__if) ).

thf(637,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(638,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if ) ),
    inference(cnf,[status(esa)],[637]) ).

thf(3615,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if ) ),
    inference(paramod_ordered,[status(thm)],[2206,638]) ).

thf(3616,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if ) ),
    inference(simp,[status(thm)],[3615]) ).

thf(3617,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if,
    inference(pattern_uni,[status(thm)],[3616:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(349,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(1330,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)],[349]) ).

thf(108,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(838,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)],[108]) ).

thf(473,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

thf(1577,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(410,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_1) ).

thf(1455,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(99,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(817,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)],[99]) ).

thf(374,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).

thf(1379,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

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

thf(1514,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ofield,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(259,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(1147,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)],[259]) ).

thf(122,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(870,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)],[122]) ).

thf(424,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__mono2_0) ).

thf(1479,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

thf(770,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(469,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(1568,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)],[469]) ).

thf(2565,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2206,591]) ).

thf(2566,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
    inference(simp,[status(thm)],[2565]) ).

thf(2567,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Orderings_Oorder,
    inference(pattern_uni,[status(thm)],[2566:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(1624,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(cnf,[status(esa)],[1623]) ).

thf(3008,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Orderings_Oorder )
       != ( A @ class_Orderings_Oorder ) )
      | ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2567,1624]) ).

thf(3009,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Orderings_Oorder )
       != ( A @ class_Orderings_Oorder ) )
      | ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[3008]) ).

thf(3010,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(pattern_uni,[status(thm)],[3009:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).

thf(3014,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[3010]) ).

thf(15,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(595,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(596,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(cnf,[status(esa)],[595]) ).

thf(2022,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(paramod_ordered,[status(thm)],[1837,596]) ).

thf(2023,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(simp,[status(thm)],[2022]) ).

thf(2024,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(pattern_uni,[status(thm)],[2023:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(431,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__iff1_1) ).

thf(1494,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(365,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(1362,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)],[365]) ).

thf(3600,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_Osgn__if ) ),
    inference(paramod_ordered,[status(thm)],[1041,638]) ).

thf(3601,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_Osgn__if ) ),
    inference(simp,[status(thm)],[3600]) ).

thf(3602,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if,
    inference(pattern_uni,[status(thm)],[3601:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

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

thf(883,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(1762,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(paramod_ordered,[status(thm)],[883,571]) ).

thf(1763,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(simp,[status(thm)],[1762]) ).

thf(1764,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add,
    inference(pattern_uni,[status(thm)],[1763:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(1968,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(paramod_ordered,[status(thm)],[1764,571]) ).

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

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

thf(2126,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(paramod_ordered,[status(thm)],[1970,571]) ).

thf(2127,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(simp,[status(thm)],[2126]) ).

thf(2128,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add,
    inference(pattern_uni,[status(thm)],[2127:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2460,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(paramod_ordered,[status(thm)],[2128,571]) ).

thf(2461,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(simp,[status(thm)],[2460]) ).

thf(2462,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add,
    inference(pattern_uni,[status(thm)],[2461:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2827,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(paramod_ordered,[status(thm)],[2462,571]) ).

thf(2828,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(simp,[status(thm)],[2827]) ).

thf(2829,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add,
    inference(pattern_uni,[status(thm)],[2828:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(115,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Polynomial_Opos__poly ) )
      | ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opos__poly ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__poly__pCons_2) ).

thf(853,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ c_Polynomial_Opos__poly ) )
      | ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opos__poly ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(309,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Opordered__comm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).

thf(1247,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Opordered__comm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(19,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(604,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)],[19]) ).

thf(605,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)],[604]) ).

thf(606,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)],[605]) ).

thf(357,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(1347,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)],[357]) ).

thf(471,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_2) ).

thf(1572,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
      | ( A = B )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(555,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(1741,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)],[555]) ).

thf(383,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(1398,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)],[383]) ).

thf(301,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(1232,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)],[301]) ).

thf(4006,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_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(paramod_ordered,[status(thm)],[1041,643]) ).

thf(4007,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(simp,[status(thm)],[4006]) ).

thf(4008,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(pattern_uni,[status(thm)],[4007:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(4430,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)],[1041,650]) ).

thf(4431,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)],[4430]) ).

thf(4432,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom,
    inference(pattern_uni,[status(thm)],[4431:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(391,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(1415,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)],[391]) ).

thf(88,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

thf(789,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(371,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(1373,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)],[371]) ).

thf(499,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).

thf(1632,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(2648,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2206,2477]) ).

thf(2649,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2648]) ).

thf(2650,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[2649:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(25,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).

thf(621,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(622,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__field ) ),
    inference(cnf,[status(esa)],[621]) ).

thf(623,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_RealVector_Oreal__normed__field )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(lifteq,[status(thm)],[622]) ).

thf(35,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

thf(646,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(106,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(834,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)],[106]) ).

thf(522,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(1677,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)],[522]) ).

thf(530,axiom,
    tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons_Ohyps_0) ).

thf(1695,plain,
    tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).

thf(4274,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ $true
      | ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(paramod_ordered,[status(thm)],[1695,568]) ).

thf(4275,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
      | ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[4274]) ).

thf(4276,plain,
    tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ),
    inference(pattern_uni,[status(thm)],[4275:[bind(A,$thf( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) ))]]) ).

thf(4394,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) ) )
      | ~ $true
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(paramod_ordered,[status(thm)],[4276,1864]) ).

thf(4395,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[4394]) ).

thf(4396,plain,
    ~ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ ( v_r @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[4395:[bind(A,$thf( v_r )),bind(B,$thf( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) ))]]) ).

thf(416,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(1465,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)],[416]) ).

thf(335,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).

thf(1302,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(515,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(1664,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)],[515]) ).

thf(2344,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[2094,587]) ).

thf(2345,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(simp,[status(thm)],[2344]) ).

thf(2346,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add,
    inference(pattern_uni,[status(thm)],[2345:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2792,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[2346,587]) ).

thf(2793,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(simp,[status(thm)],[2792]) ).

thf(2794,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add,
    inference(pattern_uni,[status(thm)],[2793:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2322,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)],[2043,608]) ).

thf(2323,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)],[2322]) ).

thf(2324,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[2323:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(541,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(1714,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)],[541]) ).

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

thf(576,plain,
    ! [A: $i] :
      ( ~ ( A @ class_HOL_Ozero )
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(577,plain,
    ! [A: $i] :
      ( ~ ( A @ class_HOL_Ozero )
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(cnf,[status(esa)],[576]) ).

thf(1846,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(paramod_ordered,[status(thm)],[1441,577]) ).

thf(1847,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(simp,[status(thm)],[1846]) ).

thf(1848,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_HOL_Ozero,
    inference(pattern_uni,[status(thm)],[1847:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(2025,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(paramod_ordered,[status(thm)],[1848,577]) ).

thf(2026,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(simp,[status(thm)],[2025]) ).

thf(2027,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero,
    inference(pattern_uni,[status(thm)],[2026:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(4070,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ 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)],[1891,645]) ).

thf(4071,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ 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)],[4070]) ).

thf(4072,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one,
    inference(pattern_uni,[status(thm)],[4071:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(408,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(1450,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)],[408]) ).

thf(275,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(1183,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Odivision__by__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(327,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = E )
      | ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
       != ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
      | ~ ( A @ class_HOL_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__iff_1) ).

thf(1283,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C = E )
      | ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
       != ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
      | ~ ( A @ class_HOL_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(269,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).

thf(1169,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(2568,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[2206,583]) ).

thf(2569,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[2568]) ).

thf(2570,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom,
    inference(pattern_uni,[status(thm)],[2569:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(3535,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ 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 @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2570,3249]) ).

thf(3536,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ 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 @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[3535]) ).

thf(3537,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[3536:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(373,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__def_0) ).

thf(1377,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(2279,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(paramod_ordered,[status(thm)],[2027,577]) ).

thf(2280,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(simp,[status(thm)],[2279]) ).

thf(2281,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero,
    inference(pattern_uni,[status(thm)],[2280:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(1974,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)],[1782,575]) ).

thf(1975,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)],[1974]) ).

thf(1976,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[1975:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(2132,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)],[1976,575]) ).

thf(2133,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)],[2132]) ).

thf(2134,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)],[2133:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2481,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)],[2134,575]) ).

thf(2482,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)],[2481]) ).

thf(2483,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)],[2482:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(244,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(1119,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)],[244]) ).

thf(359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

thf(1351,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(40,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ 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_power__divide_0) ).

thf(658,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ 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)],[40]) ).

thf(659,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(cnf,[status(esa)],[658]) ).

thf(660,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) ) ),
    inference(lifteq,[status(thm)],[659]) ).

thf(186,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(998,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)],[186]) ).

thf(181,axiom,
    tc_RealDef_Oreal @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).

thf(988,plain,
    tc_RealDef_Oreal @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(399,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

thf(1433,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(113,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(849,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(445,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(1521,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)],[445]) ).

thf(531,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(1696,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)],[531]) ).

thf(18,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oidom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors) ).

thf(602,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oidom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(79,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(766,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)],[79]) ).

thf(293,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(1215,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)],[293]) ).

thf(29,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

thf(632,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(633,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[632]) ).

thf(634,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(lifteq,[status(thm)],[633]) ).

thf(2148,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)],[1989,579]) ).

thf(2149,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)],[2148]) ).

thf(2150,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)],[2149:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2521,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)],[2150,579]) ).

thf(2522,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)],[2521]) ).

thf(2523,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)],[2522:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(222,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

thf(1072,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(2101,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1837,2040]) ).

thf(2102,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2101]) ).

thf(2103,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[2102:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(385,axiom,
    ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).

thf(1404,plain,
    ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(1405,plain,
    ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(polarity_switch,[status(thm)],[1404]) ).

thf(550,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).

thf(1732,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).

thf(1941,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[1732,581]) ).

thf(1942,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(simp,[status(thm)],[1941]) ).

thf(1943,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add,
    inference(pattern_uni,[status(thm)],[1942:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(285,axiom,
    tc_Complex_Ocomplex @ class_Int_Onumber__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

thf(1201,plain,
    tc_Complex_Ocomplex @ class_Int_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(509,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(1651,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)],[509]) ).

thf(288,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(1206,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)],[288]) ).

thf(160,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).

thf(942,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(151,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

thf(925,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(1306,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(polarity_switch,[status(thm)],[1305]) ).

thf(284,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

thf(1199,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(17,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(600,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)],[17]) ).

thf(601,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring ) ),
    inference(cnf,[status(esa)],[600]) ).

thf(2116,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)],[1041,601]) ).

thf(2117,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)],[2116]) ).

thf(2118,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring,
    inference(pattern_uni,[status(thm)],[2117:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(352,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(1338,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)],[352]) ).

thf(339,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(1311,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)],[339]) ).

thf(501,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(1636,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)],[501]) ).

thf(401,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(1438,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).

thf(661,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( D @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(262,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(1153,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)],[262]) ).

thf(77,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

thf(761,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
       != ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

thf(1067,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( B
       != ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(603,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oidom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(cnf,[status(esa)],[602]) ).

thf(2788,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(paramod_ordered,[status(thm)],[2340,603]) ).

thf(2789,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(simp,[status(thm)],[2788]) ).

thf(2790,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    inference(pattern_uni,[status(thm)],[2789:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2295,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[2046,587]) ).

thf(2296,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(simp,[status(thm)],[2295]) ).

thf(2297,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add,
    inference(pattern_uni,[status(thm)],[2296:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2658,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[2297,587]) ).

thf(2659,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add )
       != ( A @ class_OrderedGroup_Ocancel__comm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add ) ),
    inference(simp,[status(thm)],[2658]) ).

thf(2660,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__comm__monoid__add,
    inference(pattern_uni,[status(thm)],[2659:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(60,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(714,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)],[60]) ).

thf(209,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(1047,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)],[209]) ).

thf(266,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(1163,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)],[266]) ).

thf(323,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).

thf(1274,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(232,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).

thf(1091,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(196,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(1021,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)],[196]) ).

thf(474,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(1580,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)],[474]) ).

thf(246,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__less_0) ).

thf(1123,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(516,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(1666,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)],[516]) ).

thf(52,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring) ).

thf(693,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(465,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).

thf(1560,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(1387,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(cnf,[status(esa)],[1386]) ).

thf(144,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(910,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)],[144]) ).

thf(167,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(957,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)],[167]) ).

thf(135,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

thf(894,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(102,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(825,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)],[102]) ).

thf(2201,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2021,591]) ).

thf(2202,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
    inference(simp,[status(thm)],[2201]) ).

thf(2203,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Orderings_Oorder,
    inference(pattern_uni,[status(thm)],[2202:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2554,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Orderings_Oorder )
       != ( A @ class_Orderings_Oorder ) )
      | ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2203,1624]) ).

thf(2555,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Orderings_Oorder )
       != ( A @ class_Orderings_Oorder ) )
      | ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2554]) ).

thf(2556,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(pattern_uni,[status(thm)],[2555:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).

thf(2560,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2556]) ).

thf(207,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(1042,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)],[207]) ).

thf(444,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(1519,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)],[444]) ).

thf(470,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(1570,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)],[470]) ).

thf(271,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

thf(1174,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(294,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

thf(1217,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(1795,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(paramod_ordered,[status(thm)],[1137,577]) ).

thf(1796,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(simp,[status(thm)],[1795]) ).

thf(1797,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_HOL_Ozero,
    inference(pattern_uni,[status(thm)],[1796:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(1977,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(paramod_ordered,[status(thm)],[1797,577]) ).

thf(1978,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(simp,[status(thm)],[1977]) ).

thf(1979,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero,
    inference(pattern_uni,[status(thm)],[1978:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(2145,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(paramod_ordered,[status(thm)],[1979,577]) ).

thf(2146,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(simp,[status(thm)],[2145]) ).

thf(2147,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero,
    inference(pattern_uni,[status(thm)],[2146:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(435,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(1502,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)],[435]) ).

thf(100,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(820,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)],[100]) ).

thf(370,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(1370,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)],[370]) ).

thf(2013,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1837,1933]) ).

thf(2014,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2013]) ).

thf(2015,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[2014:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(549,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

thf(1731,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(286,axiom,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__norm__iff_0) ).

thf(1202,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(1203,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(cnf,[status(esa)],[1202]) ).

thf(1934,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector )
       != ( A @ class_RealVector_Oreal__normed__vector ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1731,1203]) ).

thf(1935,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector )
       != ( A @ class_RealVector_Oreal__normed__vector ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1934]) ).

thf(1936,plain,
    ~ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[1935:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(3790,plain,
    ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1101,1936]) ).

thf(3791,plain,
    ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
   != ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[3790]) ).

thf(3911,plain,
    ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
    | ( ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) )
     != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) ) )
    | ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )
     != ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[3791]) ).

thf(3958,plain,
    ( ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) )
   != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) ) ),
    inference(simp,[status(thm)],[3911]) ).

thf(367,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(1365,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)],[367]) ).

thf(2113,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[1943,581]) ).

thf(2114,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(simp,[status(thm)],[2113]) ).

thf(2115,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add,
    inference(pattern_uni,[status(thm)],[2114:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(2349,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[2115,581]) ).

thf(2350,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(simp,[status(thm)],[2349]) ).

thf(2351,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add,
    inference(pattern_uni,[status(thm)],[2350:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2824,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[2351,581]) ).

thf(2825,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(simp,[status(thm)],[2824]) ).

thf(2826,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add,
    inference(pattern_uni,[status(thm)],[2825:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(30,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add) ).

thf(635,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(636,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(cnf,[status(esa)],[635]) ).

thf(3554,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[1837,636]) ).

thf(3555,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(simp,[status(thm)],[3554]) ).

thf(3556,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add,
    inference(pattern_uni,[status(thm)],[3555:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(332,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(1296,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)],[332]) ).

thf(2179,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[1995,589]) ).

thf(2180,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2179]) ).

thf(2181,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult,
    inference(pattern_uni,[status(thm)],[2180:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(290,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(1210,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)],[290]) ).

thf(48,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(682,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)],[48]) ).

thf(249,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(1128,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(330,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

thf(1291,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(554,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).

thf(1740,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(112,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).

thf(847,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(2301,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(paramod_ordered,[status(thm)],[2049,573]) ).

thf(2302,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[2301]) ).

thf(2303,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(pattern_uni,[status(thm)],[2302:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2756,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2303,589]) ).

thf(2757,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2756]) ).

thf(2758,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult,
    inference(pattern_uni,[status(thm)],[2757:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(1602,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(cnf,[status(esa)],[1601]) ).

thf(526,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(1687,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)],[526]) ).

thf(411,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(1457,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)],[411]) ).

thf(2198,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2021,2104]) ).

thf(2199,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2198]) ).

thf(2200,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[2199:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(226,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(1079,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)],[226]) ).

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 @ ( 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(1234,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)],[302]) ).

thf(23,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(615,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)],[23]) ).

thf(219,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).

thf(1064,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(2028,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(paramod_ordered,[status(thm)],[1867,585]) ).

thf(2029,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(simp,[status(thm)],[2028]) ).

thf(2030,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom,
    inference(pattern_uni,[status(thm)],[2029:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(2282,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(paramod_ordered,[status(thm)],[2030,585]) ).

thf(2283,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(simp,[status(thm)],[2282]) ).

thf(2284,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom,
    inference(pattern_uni,[status(thm)],[2283:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2629,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(paramod_ordered,[status(thm)],[2284,585]) ).

thf(2630,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom ) ),
    inference(simp,[status(thm)],[2629]) ).

thf(2631,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom,
    inference(pattern_uni,[status(thm)],[2630:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(255,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(1138,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)],[255]) ).

thf(562,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(1755,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)],[562]) ).

thf(182,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(989,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)],[182]) ).

thf(3016,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(paramod_ordered,[status(thm)],[1995,628]) ).

thf(3017,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(simp,[status(thm)],[3016]) ).

thf(3018,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(pattern_uni,[status(thm)],[3017:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(124,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( B @ ( A @ c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1 ) @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Rats__dense__in__nn__real_2) ).

thf(874,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( B @ ( A @ c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1 ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(320,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(1270,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(315,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(1259,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)],[315]) ).

thf(163,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

thf(948,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(452,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(1534,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)],[452]) ).

thf(194,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero_0) ).

thf(1017,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(2484,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(paramod_ordered,[status(thm)],[2147,577]) ).

thf(2485,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(simp,[status(thm)],[2484]) ).

thf(2486,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero,
    inference(pattern_uni,[status(thm)],[2485:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2839,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(paramod_ordered,[status(thm)],[2486,577]) ).

thf(2840,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(simp,[status(thm)],[2839]) ).

thf(2841,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero,
    inference(pattern_uni,[status(thm)],[2840:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(347,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(1328,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(372,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

thf(1375,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(245,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ c_RealDef_Oreal__of__preal @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__all__preal_0) ).

thf(1121,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ c_RealDef_Oreal__of__preal @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(4787,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2021,655]) ).

thf(4788,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    inference(simp,[status(thm)],[4787]) ).

thf(4789,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Orderings_Opreorder,
    inference(pattern_uni,[status(thm)],[4788:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(4046,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)],[1343,645]) ).

thf(4047,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)],[4046]) ).

thf(4048,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one,
    inference(pattern_uni,[status(thm)],[4047:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(64,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(725,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)],[64]) ).

thf(178,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

thf(980,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(477,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(1587,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)],[477]) ).

thf(235,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(1096,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)],[235]) ).

thf(519,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) ).

thf(1672,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(455,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

thf(1540,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(190,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(1006,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)],[190]) ).

thf(468,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).

thf(1567,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(265,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(1160,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)],[265]) ).

thf(200,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(1028,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)],[200]) ).

thf(364,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).

thf(1361,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(156,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(933,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)],[156]) ).

thf(74,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add) ).

thf(753,plain,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(413,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(1461,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)],[413]) ).

thf(292,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

thf(1214,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(406,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(1446,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)],[406]) ).

thf(4442,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2021,650]) ).

thf(4443,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[4442]) ).

thf(4444,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__semidom,
    inference(pattern_uni,[status(thm)],[4443:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(263,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(1155,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)],[263]) ).

thf(57,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(706,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)],[57]) ).

thf(348,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(1329,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(139,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(901,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)],[139]) ).

thf(224,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_1) ).

thf(1075,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(395,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

thf(1424,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(2310,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2049,589]) ).

thf(2311,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2310]) ).

thf(2312,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult,
    inference(pattern_uni,[status(thm)],[2311:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(390,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).

thf(1414,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(2016,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ 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)],[1837,591]) ).

thf(2017,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Oorder ) ),
    inference(simp,[status(thm)],[2016]) ).

thf(2018,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Orderings_Oorder,
    inference(pattern_uni,[status(thm)],[2017:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(2190,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Orderings_Oorder )
       != ( A @ class_Orderings_Oorder ) )
      | ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2018,1624]) ).

thf(2191,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Orderings_Oorder )
       != ( A @ class_Orderings_Oorder ) )
      | ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2190]) ).

thf(2192,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(pattern_uni,[status(thm)],[2191:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).

thf(2196,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2192]) ).

thf(4052,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ 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)],[1825,645]) ).

thf(4053,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ 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)],[4052]) ).

thf(4054,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one,
    inference(pattern_uni,[status(thm)],[4053:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(47,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(679,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)],[47]) ).

thf(205,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(1039,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)],[205]) ).

thf(173,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

thf(970,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

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_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).

thf(1419,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)],[393]) ).

thf(3240,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2570,2781]) ).

thf(3241,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[3240]) ).

thf(3242,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[3241:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(317,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(1263,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)],[317]) ).

thf(180,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__sgn_0) ).

thf(985,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Osgn__class_Osgn ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(260,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(1150,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)],[260]) ).

thf(281,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).

thf(1192,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(211,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(1050,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)],[211]) ).

thf(1832,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)],[1360,575]) ).

thf(1833,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)],[1832]) ).

thf(1834,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[1833:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(2010,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)],[1834,575]) ).

thf(2011,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)],[2010]) ).

thf(2012,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring__1,
    inference(pattern_uni,[status(thm)],[2011:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(4932,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)],[2012,657]) ).

thf(4933,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)],[4932]) ).

thf(4934,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[4933:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(188,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).

thf(1002,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
      = ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(544,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(1720,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)],[544]) ).

thf(2966,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)],[2523,579]) ).

thf(2967,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)],[2966]) ).

thf(2968,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)],[2967:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(345,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

thf(1324,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(450,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Oln @ ( A @ c_Transcendental_Oln @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ln__le__cancel__iff_0) ).

thf(1530,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Oln @ ( A @ c_Transcendental_Oln @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(376,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Oln @ ( A @ c_Transcendental_Oln @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ln__less__cancel__iff_0) ).

thf(1382,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Oln @ ( A @ c_Transcendental_Oln @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(318,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

thf(1266,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(2151,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[1992,581]) ).

thf(2152,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(simp,[status(thm)],[2151]) ).

thf(2153,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add,
    inference(pattern_uni,[status(thm)],[2152:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(251,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(1131,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(3758,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1101,1864]) ).

thf(3759,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[3758]) ).

thf(3760,plain,
    ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ c_lessequals ) ) ),
    inference(pattern_uni,[status(thm)],[3759:[bind(A,$thf( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )),bind(B,$thf( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) ))]]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ v_x @ ( tc_Complex_Ocomplex @ ( v_cs____ @ ( v_c____ @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(567,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ v_x @ ( tc_Complex_Ocomplex @ ( v_cs____ @ ( v_c____ @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(569,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ v_x @ ( tc_Complex_Ocomplex @ ( v_cs____ @ ( v_c____ @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(cnf,[status(esa)],[567]) ).

thf(397,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(1429,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)],[397]) ).

thf(84,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(779,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)],[84]) ).

thf(4067,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)],[1546,645]) ).

thf(4068,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)],[4067]) ).

thf(4069,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one,
    inference(pattern_uni,[status(thm)],[4068:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(564,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(1759,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)],[564]) ).

thf(381,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(1393,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)],[381]) ).

thf(497,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(1627,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)],[497]) ).

thf(447,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).

thf(1525,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(350,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(1333,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)],[350]) ).

thf(342,axiom,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_cs____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons_Ohyps_1) ).

thf(1318,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_cs____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(306,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(1241,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)],[306]) ).

thf(149,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(921,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(198,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(1026,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(2187,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)],[2012,575]) ).

thf(2188,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)],[2187]) ).

thf(2189,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)],[2188:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2527,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[2153,581]) ).

thf(2528,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(simp,[status(thm)],[2527]) ).

thf(2529,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add,
    inference(pattern_uni,[status(thm)],[2528:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(322,axiom,
    tc_RealDef_Oreal @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).

thf(1273,plain,
    tc_RealDef_Oreal @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(204,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(1037,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)],[204]) ).

thf(1038,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(cnf,[status(esa)],[1037]) ).

thf(1808,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Orderings_Opreorder )
       != ( A @ class_Orderings_Opreorder ) )
      | ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1273,1038]) ).

thf(1809,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Orderings_Opreorder )
       != ( A @ class_Orderings_Opreorder ) )
      | ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1808]) ).

thf(1810,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(pattern_uni,[status(thm)],[1809:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(1814,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1810]) ).

thf(3805,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1101,1814]) ).

thf(3806,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[3805]) ).

thf(3807,plain,
    ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[3806:[bind(A,$thf( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )),bind(B,$thf( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) ))]]) ).

thf(2632,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(paramod_ordered,[status(thm)],[2284,603]) ).

thf(2633,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(simp,[status(thm)],[2632]) ).

thf(2634,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    inference(pattern_uni,[status(thm)],[2633:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2747,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(paramod_ordered,[status(thm)],[2303,573]) ).

thf(2748,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[2747]) ).

thf(2749,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(pattern_uni,[status(thm)],[2748:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(89,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ 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_add__num__frac_0) ).

thf(792,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( D
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oinverse__class_Odivide ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ 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)],[89]) ).

thf(158,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(938,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)],[158]) ).

thf(540,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(1712,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)],[540]) ).

thf(214,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Oln @ ( A @ c_Transcendental_Oln @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ln__le__cancel__iff_1) ).

thf(1054,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ c_Transcendental_Oln @ ( A @ c_Transcendental_Oln @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(328,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(1286,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)],[328]) ).

thf(203,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(1035,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)],[203]) ).

thf(441,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

thf(1515,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(2219,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(paramod_ordered,[status(thm)],[2021,596]) ).

thf(2220,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(simp,[status(thm)],[2219]) ).

thf(2221,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(pattern_uni,[status(thm)],[2220:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(82,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(773,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)],[82]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

thf(1135,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(1999,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ 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)],[1825,589]) ).

thf(2000,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ 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)],[1999]) ).

thf(2001,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult,
    inference(pattern_uni,[status(thm)],[2000:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(532,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

thf(1698,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).

thf(3040,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_Ocomm__monoid__mult ) ),
    inference(paramod_ordered,[status(thm)],[1546,628]) ).

thf(3041,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_Ocomm__monoid__mult ) ),
    inference(simp,[status(thm)],[3040]) ).

thf(3042,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(pattern_uni,[status(thm)],[3041:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(295,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(1219,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)],[295]) ).

thf(481,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(1595,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)],[481]) ).

thf(4190,plain,
    ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ ( v_r @ c_HOL_Oord__class_Oless ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1695,3980]) ).

thf(4191,plain,
    ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
   != ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ ( v_r @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[4190]) ).

thf(4316,plain,
    ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
    | ( ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) )
     != ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) ) )
    | ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )
     != v_r ) ),
    inference(simp,[status(thm)],[4191]) ).

thf(4365,plain,
    ( ( ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) )
     != ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) ) )
    | ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )
     != v_r ) ),
    inference(simp,[status(thm)],[4316]) ).

thf(67,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).

thf(733,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(141,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).

thf(906,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(171,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(965,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)],[171]) ).

thf(73,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(750,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)],[73]) ).

thf(547,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(1727,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)],[547]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

thf(618,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(4917,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)],[2189,657]) ).

thf(4918,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)],[4917]) ).

thf(4919,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)],[4918:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(258,axiom,
    tc_Complex_Ocomplex @ class_Power_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).

thf(1146,plain,
    tc_Complex_Ocomplex @ class_Power_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(561,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(1754,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(140,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(904,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)],[140]) ).

thf(492,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(1615,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)],[492]) ).

thf(2655,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)],[2290,608]) ).

thf(2656,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)],[2655]) ).

thf(2657,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)],[2656:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(560,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(1752,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)],[560]) ).

thf(379,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(1388,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)],[379]) ).

thf(533,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

thf(1701,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(1520,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)],[1519]) ).

thf(4941,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)],[1976,657]) ).

thf(4942,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)],[4941]) ).

thf(4943,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[4942:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(110,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(843,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)],[110]) ).

thf(247,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).

thf(1125,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(59,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
        = ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__mult_0) ).

thf(711,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
        = ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(428,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(1488,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)],[428]) ).

thf(32,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).

thf(639,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(640,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(cnf,[status(esa)],[639]) ).

thf(641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_RealVector_Oreal__normed__algebra )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(lifteq,[status(thm)],[640]) ).

thf(517,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(1669,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(157,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(936,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)],[157]) ).

thf(536,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(1707,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)],[536]) ).

thf(321,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(1271,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)],[321]) ).

thf(21,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_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).

thf(609,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_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(610,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_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(cnf,[status(esa)],[609]) ).

thf(611,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom )
      | ( ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(lifteq,[status(thm)],[610]) ).

thf(305,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(1239,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)],[305]) ).

thf(231,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(1090,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(415,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(1464,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(3566,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[2206,636]) ).

thf(3567,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(simp,[status(thm)],[3566]) ).

thf(3568,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add,
    inference(pattern_uni,[status(thm)],[3567:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(521,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(1675,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)],[521]) ).

thf(500,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(1635,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(551,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(1733,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)],[551]) ).

thf(2053,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ 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)],[1891,589]) ).

thf(2054,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ 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)],[2053]) ).

thf(2055,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult,
    inference(pattern_uni,[status(thm)],[2054:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(233,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(1092,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)],[233]) ).

thf(1895,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)],[1343,589]) ).

thf(1896,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)],[1895]) ).

thf(1897,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult,
    inference(pattern_uni,[status(thm)],[1896:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(148,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(919,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)],[148]) ).

thf(94,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__commutes_0) ).

thf(804,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Omonoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(502,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__trans_0) ).

thf(1638,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( C @ ( A @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( C @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(297,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).

thf(1224,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(2571,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2206,601]) ).

thf(2572,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2571]) ).

thf(2573,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring,
    inference(pattern_uni,[status(thm)],[2572:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(361,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

thf(1356,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(105,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
       != ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
      | ~ ( A @ class_HOL_Ozero ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons__eq__iff_0) ).

thf(831,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) )
       != ( A @ ( E @ ( D @ c_Polynomial_OpCons ) ) ) )
      | ~ ( A @ class_HOL_Ozero ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(387,axiom,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_cs____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pCons_1) ).

thf(1408,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_cs____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(326,axiom,
    tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( v_m____ @ ( v_r @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( v_c____ @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).

thf(1282,plain,
    tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( v_m____ @ ( v_r @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( v_c____ @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(1892,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)],[1546,589]) ).

thf(1893,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)],[1892]) ).

thf(1894,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult,
    inference(pattern_uni,[status(thm)],[1893:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(86,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(784,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)],[86]) ).

thf(192,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(1011,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)],[192]) ).

thf(68,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

thf(736,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(358,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(1349,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)],[358]) ).

thf(456,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(1542,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)],[456]) ).

thf(528,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).

thf(1690,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(337,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(1307,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)],[337]) ).

thf(119,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(863,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)],[119]) ).

thf(78,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(764,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)],[78]) ).

thf(478,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(1589,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)],[478]) ).

thf(185,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_1) ).

thf(996,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(430,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(1492,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)],[430]) ).

thf(485,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(1603,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)],[485]) ).

thf(545,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) )
        = ( A @ ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__pCons_0) ).

thf(1722,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) )
        = ( A @ ( A @ ( A @ ( D @ ( C @ c_Polynomial_Opoly ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(257,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(1144,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)],[257]) ).

thf(127,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(880,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)],[127]) ).

thf(598,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)],[597]) ).

thf(599,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)],[598]) ).

thf(402,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(1439,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)],[402]) ).

thf(133,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

thf(890,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

thf(97,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

thf(811,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(630,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[629]) ).

thf(631,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(lifteq,[status(thm)],[630]) ).

thf(117,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(858,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)],[117]) ).

thf(498,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_Osgn__class_Osgn ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__less_1) ).

thf(1630,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_Osgn__class_Osgn ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(2778,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2206,2651]) ).

thf(2779,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2778]) ).

thf(2780,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[2779:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(55,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ 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_add__frac__num_0) ).

thf(700,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ 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)],[55]) ).

thf(3612,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if ) ),
    inference(paramod_ordered,[status(thm)],[2021,638]) ).

thf(3613,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if ) ),
    inference(simp,[status(thm)],[3612]) ).

thf(3614,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if,
    inference(pattern_uni,[status(thm)],[3613:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(26,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).

thf(624,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(625,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[624]) ).

thf(626,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( ( A @ ( C @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(lifteq,[status(thm)],[625]) ).

thf(355,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(1344,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)],[355]) ).

thf(463,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(1556,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)],[463]) ).

thf(2972,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[2529,581]) ).

thf(2973,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add )
       != ( A @ class_OrderedGroup_Ocomm__monoid__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(simp,[status(thm)],[2972]) ).

thf(2974,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__add,
    inference(pattern_uni,[status(thm)],[2973:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(217,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(1061,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)],[217]) ).

thf(1875,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector )
       != ( A @ class_RealVector_Oreal__normed__vector ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1515,1203]) ).

thf(1876,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector )
       != ( A @ class_RealVector_Oreal__normed__vector ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1875]) ).

thf(1877,plain,
    ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[1876:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(419,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(1471,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)],[419]) ).

thf(76,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).

thf(758,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(3025,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(paramod_ordered,[status(thm)],[2172,628]) ).

thf(3026,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(simp,[status(thm)],[3025]) ).

thf(3027,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(pattern_uni,[status(thm)],[3026:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2341,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(paramod_ordered,[status(thm)],[2091,603]) ).

thf(2342,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(simp,[status(thm)],[2341]) ).

thf(2343,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    inference(pattern_uni,[status(thm)],[2342:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2623,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(paramod_ordered,[status(thm)],[2281,577]) ).

thf(2624,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero )
       != ( A @ class_HOL_Ozero ) )
      | ( A @ tc_Polynomial_Opoly @ class_HOL_Ozero ) ),
    inference(simp,[status(thm)],[2623]) ).

thf(2625,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_HOL_Ozero,
    inference(pattern_uni,[status(thm)],[2624:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(2105,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Orderings_Oorder )
       != ( A @ class_Orderings_Oorder ) )
      | ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1921,1624]) ).

thf(2106,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Orderings_Oorder )
       != ( A @ class_Orderings_Oorder ) )
      | ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2105]) ).

thf(2107,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(pattern_uni,[status(thm)],[2106:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly )),bind(B,$thf( B )),bind(C,$thf( C ))]]) ).

thf(2111,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2107]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

thf(592,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(593,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[592]) ).

thf(594,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(lifteq,[status(thm)],[593]) ).

thf(92,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

thf(799,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Oab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(3767,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1101,1306]) ).

thf(3768,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[3767]) ).

thf(3885,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) )
       != A )
      | ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )
       != A ) ),
    inference(simp,[status(thm)],[3768]) ).

thf(3932,plain,
    ( ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) )
   != ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
    inference(simp,[status(thm)],[3885]) ).

thf(331,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ c_Transcendental_Oln )
       != ( B @ c_Transcendental_Oln ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ln__inj__iff_0) ).

thf(1293,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ c_Transcendental_Oln )
       != ( B @ c_Transcendental_Oln ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(2551,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)],[2189,575]) ).

thf(2552,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)],[2551]) ).

thf(2553,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)],[2552:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(179,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).

thf(983,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(421,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(1474,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)],[421]) ).

thf(168,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(959,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)],[168]) ).

thf(449,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(1528,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)],[449]) ).

thf(242,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(1113,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)],[242]) ).

thf(423,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

thf(1477,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(2533,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(paramod_ordered,[status(thm)],[2172,573]) ).

thf(2534,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[2533]) ).

thf(2535,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(pattern_uni,[status(thm)],[2534:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(238,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(1102,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)],[238]) ).

thf(2154,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(paramod_ordered,[status(thm)],[1867,603]) ).

thf(2155,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(simp,[status(thm)],[2154]) ).

thf(2156,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    inference(pattern_uni,[status(thm)],[2155:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(652,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(cnf,[status(esa)],[651]) ).

thf(653,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(lifteq,[status(thm)],[652]) ).

thf(150,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(922,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)],[150]) ).

thf(466,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(1562,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)],[466]) ).

thf(145,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).

thf(912,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

thf(685,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(80,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(768,plain,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocancel__comm__monoid__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(103,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add) ).

thf(827,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(2833,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)],[2483,575]) ).

thf(2834,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)],[2833]) ).

thf(2835,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)],[2834:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(53,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Osgn__class_Osgn ) )
        = ( A @ ( B @ c_HOL_Osgn__class_Osgn ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).

thf(695,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Osgn__class_Osgn ) )
        = ( A @ ( B @ c_HOL_Osgn__class_Osgn ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(308,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ c_RealDef_Oreal__of__preal @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__less__all__real2_0) ).

thf(1245,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ c_RealDef_Oreal__of__preal @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(272,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

thf(1176,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(187,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

thf(1000,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( B @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(400,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(1435,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)],[400]) ).

thf(366,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).

thf(1364,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(311,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).

thf(1250,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(432,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).

thf(1496,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(2003,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_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(paramod_ordered,[status(thm)],[1041,596]) ).

thf(2004,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(simp,[status(thm)],[2003]) ).

thf(2005,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(pattern_uni,[status(thm)],[2004:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(63,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).

thf(722,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_Power_Opower__class_Opower ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_Power_Opower__class_Opower ) ) @ ( A @ ( D @ ( B @ c_Power_Opower__class_Opower ) ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(202,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(1033,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)],[202]) ).

thf(1034,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(cnf,[status(esa)],[1033]) ).

thf(4905,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)],[1782,657]) ).

thf(4906,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)],[4905]) ).

thf(4907,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[4906:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(514,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( 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__power_0) ).

thf(1662,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( 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)],[514]) ).

thf(161,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(944,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)],[161]) ).

thf(417,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(1467,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)],[417]) ).

thf(152,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

thf(927,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__field,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(525,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( A
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__left__cancel_0) ).

thf(1684,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( A
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(647,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add ) ),
    inference(cnf,[status(esa)],[646]) ).

thf(648,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocancel__ab__semigroup__add )
      | ( C = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(lifteq,[status(thm)],[647]) ).

thf(438,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(1509,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)],[438]) ).

thf(227,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(1081,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)],[227]) ).

thf(616,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(cnf,[status(esa)],[615]) ).

thf(617,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Odivision__by__zero )
      | ~ ( A @ class_Ring__and__Field_Ofield )
      | ( ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oinverse__class_Odivide ) ) )
        = ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Otimes__class_Otimes ) ) ) ) ),
    inference(lifteq,[status(thm)],[616]) ).

thf(2331,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)],[1473,608]) ).

thf(2332,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)],[2331]) ).

thf(2333,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[2332:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(172,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(968,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)],[172]) ).

thf(1787,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)],[1063,1520]) ).

thf(1788,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)],[1787]) ).

thf(1789,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[1788:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(1790,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)],[1789]) ).

thf(2071,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_RealDef_Oreal @ ( E @ ( E @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(paramod_ordered,[status(thm)],[599,1790]) ).

thf(2072,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(pattern_uni,[status(thm)],[2071:[bind(A,$thf( tc_RealDef_Oreal )),bind(B,$thf( I )),bind(C,$thf( J )),bind(D,$thf( tc_RealDef_Oreal @ ( J @ ( I @ c_HOL_Otimes__class_Otimes ) ) )),bind(E,$thf( tc_RealDef_Oreal @ ( J @ ( I @ c_HOL_Otimes__class_Otimes ) ) ))]]) ).

thf(2083,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( 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)],[2072]) ).

thf(3570,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(rewrite,[status(thm)],[2083,1546]) ).

thf(3571,plain,
    ! [B: $i,A: $i] :
      ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[3570]) ).

thf(210,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).

thf(1049,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocancel__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(563,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(1758,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ozero__neq__one,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(267,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(1166,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)],[267]) ).

thf(289,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(1208,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)],[289]) ).

thf(90,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Omonoid__add) ).

thf(795,plain,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(2316,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)],[1803,608]) ).

thf(2317,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)],[2316]) ).

thf(2318,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[2317:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(324,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(1277,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)],[324]) ).

thf(2122,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ 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)],[1837,601]) ).

thf(2123,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ 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)],[2122]) ).

thf(2124,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring,
    inference(pattern_uni,[status(thm)],[2123:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(107,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(836,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)],[107]) ).

thf(461,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1 ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Rats__dense__in__nn__real_1) ).

thf(1551,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1 ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(4043,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2049,645]) ).

thf(4044,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[4043]) ).

thf(4045,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one,
    inference(pattern_uni,[status(thm)],[4044:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(4935,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)],[1834,657]) ).

thf(4936,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)],[4935]) ).

thf(4937,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[4936:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(556,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(1743,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)],[556]) ).

thf(132,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(887,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)],[132]) ).

thf(69,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osemiring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring) ).

thf(739,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osemiring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(236,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(1098,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)],[236]) ).

thf(1842,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Orderings_Opreorder )
       != ( A @ class_Orderings_Opreorder ) )
      | ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1273,1518]) ).

thf(1843,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Orderings_Opreorder )
       != ( A @ class_Orderings_Opreorder ) )
      | ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[1842]) ).

thf(1844,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[1843:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(1845,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[1844]) ).

thf(459,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(1547,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)],[459]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

thf(776,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( B @ ( C @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(558,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(1748,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)],[558]) ).

thf(116,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(855,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)],[116]) ).

thf(442,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(1516,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(483,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult_0) ).

thf(1598,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__div__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(221,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(1070,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)],[221]) ).

thf(123,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(872,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)],[123]) ).

thf(2141,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1837,2104]) ).

thf(2142,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2141]) ).

thf(2143,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[2142:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(486,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(1605,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)],[486]) ).

thf(2586,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(paramod_ordered,[status(thm)],[2206,596]) ).

thf(2587,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(simp,[status(thm)],[2586]) ).

thf(2588,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(pattern_uni,[status(thm)],[2587:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(4920,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)],[2134,657]) ).

thf(4921,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)],[4920]) ).

thf(4922,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)],[4921:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(507,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(1647,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)],[507]) ).

thf(166,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(954,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)],[166]) ).

thf(312,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(1252,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)],[312]) ).

thf(300,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(1230,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)],[300]) ).

thf(426,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(1484,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)],[426]) ).

thf(45,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(673,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)],[45]) ).

thf(2163,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(paramod_ordered,[status(thm)],[884,603]) ).

thf(2164,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(simp,[status(thm)],[2163]) ).

thf(2165,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    inference(pattern_uni,[status(thm)],[2164:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(4018,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(paramod_ordered,[status(thm)],[2021,643]) ).

thf(4019,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(simp,[status(thm)],[4018]) ).

thf(4020,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add,
    inference(pattern_uni,[status(thm)],[4019:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(4766,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)],[1041,655]) ).

thf(4767,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)],[4766]) ).

thf(4768,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Orderings_Opreorder,
    inference(pattern_uni,[status(thm)],[4767:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(341,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).

thf(1316,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(1317,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(cnf,[status(esa)],[1316]) ).

thf(3532,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ 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 @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(paramod_ordered,[status(thm)],[583,3249]) ).

thf(3533,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( C @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( C @ 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 @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[3532]) ).

thf(3534,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(pattern_uni,[status(thm)],[3533:[bind(A,$thf( D )),bind(B,$thf( B )),bind(C,$thf( D @ tc_Polynomial_Opoly ))]]) ).

thf(3544,plain,
    ! [B: $i,A: $i] :
      ( ~ ( B @ 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 @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( B @ class_Ring__and__Field_Oordered__idom ) ),
    inference(simp,[status(thm)],[3534]) ).

thf(523,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(1679,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)],[523]) ).

thf(553,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

thf(1738,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(3078,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2570,2651]) ).

thf(3079,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[3078]) ).

thf(3080,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[3079:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(213,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).

thf(1053,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(433,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(1499,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(334,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(1300,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)],[334]) ).

thf(409,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).

thf(1452,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(278,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(1188,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(277,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(1186,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)],[277]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).

thf(1085,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(512,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(1658,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)],[512]) ).

thf(454,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(1538,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)],[454]) ).

thf(351,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(1336,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)],[351]) ).

thf(71,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(744,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)],[71]) ).

thf(314,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

thf(1257,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

thf(703,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(296,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(1221,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)],[296]) ).

thf(212,axiom,
    tc_RealDef_Oreal @ class_Power_Opower,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Power_Opower) ).

thf(1052,plain,
    tc_RealDef_Oreal @ class_Power_Opower,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(396,axiom,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( v_m____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_cs____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_m_0) ).

thf(1427,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( v_m____ @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_cs____ @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(65,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(727,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)],[65]) ).

thf(125,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(876,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)],[125]) ).

thf(183,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

thf(991,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(362,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(1358,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)],[362]) ).

thf(256,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__norm__iff_1) ).

thf(1141,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(2990,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2535,589]) ).

thf(2991,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2990]) ).

thf(2992,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Omonoid__mult,
    inference(pattern_uni,[status(thm)],[2991:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(453,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( 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__power_0) ).

thf(1536,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__semidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(197,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__zero_0) ).

thf(1023,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(476,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(1585,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)],[476]) ).

thf(234,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(1094,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)],[234]) ).

thf(518,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

thf(1670,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(3022,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_Ocomm__monoid__mult ) ),
    inference(paramod_ordered,[status(thm)],[1343,628]) ).

thf(3023,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_Ocomm__monoid__mult ) ),
    inference(simp,[status(thm)],[3022]) ).

thf(3024,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(pattern_uni,[status(thm)],[3023:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(542,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(1717,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(1878,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector )
       != ( A @ class_RealVector_Oreal__normed__vector ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1515,1317]) ).

thf(1879,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector )
       != ( A @ class_RealVector_Oreal__normed__vector ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1878]) ).

thf(1880,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[1879:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(1881,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_RealDef_Oreal @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[1880]) ).

thf(1937,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector )
       != ( A @ class_RealVector_Oreal__normed__vector ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1731,1317]) ).

thf(1938,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector )
       != ( A @ class_RealVector_Oreal__normed__vector ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[1937]) ).

thf(1939,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[1938:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(1940,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(simp,[status(thm)],[1939]) ).

thf(111,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(845,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)],[111]) ).

thf(394,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( E
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).

thf(1421,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( E
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oinverse__class_Odivide ) ) @ ( A @ ( C @ ( B @ c_HOL_Oinverse__class_Odivide ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oinverse__class_Odivide ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ofield ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(3563,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[2021,636]) ).

thf(3564,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(simp,[status(thm)],[3563]) ).

thf(3565,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add,
    inference(pattern_uni,[status(thm)],[3564:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(412,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

thf(1459,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).

thf(1180,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(155,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(931,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)],[155]) ).

thf(462,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

thf(1553,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(4163,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1695,1864]) ).

thf(4164,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[4163]) ).

thf(4165,plain,
    ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ c_lessequals ) ) ),
    inference(pattern_uni,[status(thm)],[4164:[bind(A,$thf( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )),bind(B,$thf( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) ))]]) ).

thf(389,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opos__poly ) )
      | ( A @ ( C @ c_Polynomial_Opos__poly ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pos__poly__pCons_1) ).

thf(1412,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( C @ ( B @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opos__poly ) )
      | ( A @ ( C @ c_Polynomial_Opos__poly ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(2207,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2021,601]) ).

thf(2208,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2207]) ).

thf(2209,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__semiring,
    inference(pattern_uni,[status(thm)],[2208:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(248,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(1126,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)],[248]) ).

thf(329,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(1289,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)],[329]) ).

thf(508,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_0) ).

thf(1649,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).

thf(4400,plain,
    ( ( ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
     != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ c_lessequals ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[4276,3760]) ).

thf(4401,plain,
    ( ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
   != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[4400]) ).

thf(4417,plain,
    ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
    | ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )
     != v_r )
    | ( ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) )
     != ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) ) ) ),
    inference(simp,[status(thm)],[4401]) ).

thf(4419,plain,
    ( ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )
     != v_r )
    | ( ( tc_Complex_Ocomplex @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ v_x @ c_RealVector_Onorm__class_Onorm ) )
     != ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) ) ) ),
    inference(simp,[status(thm)],[4417]) ).

thf(176,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(976,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(50,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

thf(688,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( E @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(407,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).

thf(1448,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(279,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).

thf(1189,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Osemiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(380,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(1390,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)],[380]) ).

thf(472,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(1575,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)],[472]) ).

thf(240,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(1108,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)],[240]) ).

thf(3037,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(paramod_ordered,[status(thm)],[2303,628]) ).

thf(3038,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(simp,[status(thm)],[3037]) ).

thf(3039,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(pattern_uni,[status(thm)],[3038:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(346,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(1326,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)],[346]) ).

thf(169,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(961,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)],[169]) ).

thf(170,axiom,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).

thf(963,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(422,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(1476,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(425,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(1481,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)],[425]) ).

thf(4040,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[1995,645]) ).

thf(4041,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[4040]) ).

thf(4042,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one,
    inference(pattern_uni,[status(thm)],[4041:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(557,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).

thf(1745,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(446,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

thf(1523,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(87,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

thf(786,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( C @ ( D @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_OrderedGroup_Ocancel__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(85,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(781,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)],[85]) ).

thf(2524,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)],[2150,608]) ).

thf(2525,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)],[2524]) ).

thf(2526,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)],[2525:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(464,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(1558,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)],[464]) ).

thf(4911,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)],[1027,657]) ).

thf(4912,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)],[4911]) ).

thf(4913,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Int_Onumber__ring,
    inference(pattern_uni,[status(thm)],[4912:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(353,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(1341,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)],[353]) ).

thf(136,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(896,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(162,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(946,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)],[162]) ).

thf(2969,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)],[2523,608]) ).

thf(2970,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)],[2969]) ).

thf(2971,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)],[2970:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(1855,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Orderings_Olinorder )
       != ( A @ class_Orderings_Olinorder ) )
      | ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1463,1034]) ).

thf(1856,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Orderings_Olinorder )
       != ( A @ class_Orderings_Olinorder ) )
      | ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( B @ ( B @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[1855]) ).

thf(1857,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ) ),
    inference(pattern_uni,[status(thm)],[1856:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(1861,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ) ),
    inference(simp,[status(thm)],[1857]) ).

thf(527,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).

thf(1689,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(146,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

thf(914,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(4212,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1695,1814]) ).

thf(4213,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[4212]) ).

thf(4214,plain,
    ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[4213:[bind(A,$thf( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )),bind(B,$thf( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) ))]]) ).

thf(2328,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)],[907,608]) ).

thf(2329,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)],[2328]) ).

thf(2330,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[2329:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(2574,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[2206,2144]) ).

thf(2575,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( B @ class_Ring__and__Field_Oordered__idom ) )
      | ~ ( B @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2574]) ).

thf(2576,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(pattern_uni,[status(thm)],[2575:[bind(A,$thf( A )),bind(B,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(282,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).

thf(1193,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(291,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__mono_0) ).

thf(1212,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(487,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

thf(1607,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ofield,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(138,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(899,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)],[138]) ).

thf(338,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(1309,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)],[338]) ).

thf(404,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

thf(1442,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(208,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(1045,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)],[208]) ).

thf(201,axiom,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_0) ).

thf(1030,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(429,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(1490,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)],[429]) ).

thf(1491,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(cnf,[status(esa)],[1490]) ).

thf(43,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).

thf(667,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(4772,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ 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)],[1837,655]) ).

thf(4773,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    inference(simp,[status(thm)],[4772]) ).

thf(4774,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Orderings_Opreorder,
    inference(pattern_uni,[status(thm)],[4773:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(225,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(1077,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)],[225]) ).

thf(2160,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(paramod_ordered,[status(thm)],[1644,603]) ).

thf(2161,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(simp,[status(thm)],[2160]) ).

thf(2162,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    inference(pattern_uni,[status(thm)],[2161:[bind(A,$thf( tc_Complex_Ocomplex ))]]) ).

thf(61,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(716,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)],[61]) ).

thf(491,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).

thf(1614,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(243,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

thf(1116,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(252,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(1133,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)],[252]) ).

thf(504,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(1642,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)],[504]) ).

thf(439,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

thf(1512,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(164,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(950,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)],[164]) ).

thf(310,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(1248,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)],[310]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__less__iff1_0) ).

thf(865,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( C @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(2285,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(paramod_ordered,[status(thm)],[2030,603]) ).

thf(2286,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(simp,[status(thm)],[2285]) ).

thf(2287,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    inference(pattern_uni,[status(thm)],[2286:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(619,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(cnf,[status(esa)],[618]) ).

thf(620,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) ) ),
    inference(lifteq,[status(thm)],[619]) ).

thf(546,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(1725,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)],[546]) ).

thf(325,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(1280,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)],[325]) ).

thf(382,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

thf(1395,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(496,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(1625,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)],[496]) ).

thf(480,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__mult__order_0) ).

thf(1593,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(375,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).

thf(1380,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(448,axiom,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( A @ c_RealDef_Oreal__of__preal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__of__preal__zero__less_0) ).

thf(1527,plain,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( A @ c_RealDef_Oreal__of__preal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(520,axiom,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( A @ ( A @ c_Transcendental_Oln @ c_HOL_Oord__class_Oless ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ln__less__self_0) ).

thf(1673,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( A @ ( A @ c_Transcendental_Oln @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(121,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(867,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)],[121]) ).

thf(4172,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
       != ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1695,1306]) ).

thf(4173,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[4172]) ).

thf(4308,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) )
       != A )
      | ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )
       != A ) ),
    inference(simp,[status(thm)],[4173]) ).

thf(4357,plain,
    ( ( v_r @ ( v_cs____ @ v_sko__local__XpCons__Xhyps__1 ) )
   != ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ),
    inference(simp,[status(thm)],[4308]) ).

thf(95,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Power_Opower) ).

thf(807,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Power_Opower ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(3028,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(paramod_ordered,[status(thm)],[1825,628]) ).

thf(3029,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(simp,[status(thm)],[3028]) ).

thf(3030,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(pattern_uni,[status(thm)],[3029:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(3043,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(paramod_ordered,[status(thm)],[1891,628]) ).

thf(3044,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult ) ),
    inference(simp,[status(thm)],[3043]) ).

thf(3045,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Ocomm__monoid__mult,
    inference(pattern_uni,[status(thm)],[3044:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(147,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Osgn__if,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if) ).

thf(918,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Osgn__if,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(4049,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2172,645]) ).

thf(4050,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[4049]) ).

thf(4051,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one,
    inference(pattern_uni,[status(thm)],[4050:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(270,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(1172,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)],[270]) ).

thf(137,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

thf(897,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(388,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

thf(1410,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__cancel__ab__semigroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(215,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(1056,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)],[215]) ).

thf(42,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C = E )
      | ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).

thf(664,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C = E )
      | ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) )
       != ( A @ ( A @ ( C @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( E @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(538,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(1710,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(356,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).

thf(1346,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(489,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__zero__iff_0) ).

thf(1610,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Osgn__class_Osgn ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(1742,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(cnf,[status(esa)],[1741]) ).

thf(153,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(928,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)],[153]) ).

thf(303,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(1236,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)],[303]) ).

thf(2157,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(paramod_ordered,[status(thm)],[1904,603]) ).

thf(2158,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oidom )
       != ( A @ class_Ring__and__Field_Oidom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(simp,[status(thm)],[2157]) ).

thf(2159,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring__1__no__zero__divisors,
    inference(pattern_uni,[status(thm)],[2158:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(250,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(1129,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)],[250]) ).

thf(316,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult__ineq_0) ).

thf(1261,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(475,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).

thf(1582,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_Power_Opower__class_Opower ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_Ring__and__Field_Oring__1__no__zero__divisors ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(4064,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[2303,645]) ).

thf(4065,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ 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)],[4064]) ).

thf(4066,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ozero__neq__one,
    inference(pattern_uni,[status(thm)],[4065:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(143,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(908,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)],[143]) ).

thf(434,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(1500,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)],[434]) ).

thf(101,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(822,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)],[101]) ).

thf(51,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(691,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)],[51]) ).

thf(319,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(1268,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)],[319]) ).

thf(451,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(1532,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)],[451]) ).

thf(118,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(860,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)],[118]) ).

thf(377,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

thf(1384,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(3603,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if ) ),
    inference(paramod_ordered,[status(thm)],[1837,638]) ).

thf(3604,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if ) ),
    inference(simp,[status(thm)],[3603]) ).

thf(3605,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Osgn__if,
    inference(pattern_uni,[status(thm)],[3604:[bind(A,$thf( tc_RealDef_Oreal @ tc_Polynomial_Opoly ))]]) ).

thf(3820,plain,
    ( ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
     != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) )
    | ~ $true ),
    inference(paramod_ordered,[status(thm)],[1101,1877]) ).

thf(3821,plain,
    ( ( tc_RealDef_Oreal @ ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
   != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[3820]) ).

thf(3892,plain,
    ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
    | ( ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) )
     != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) ) )
    | ( ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero )
     != ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(simp,[status(thm)],[3821]) ).

thf(3939,plain,
    ( ( v_r @ ( v_cs____ @ v_sko__local__XpCons__1 ) )
   != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_Onorm__class_Onorm ) ) ),
    inference(simp,[status(thm)],[3892]) ).

thf(114,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

thf(850,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oplus__class_Oplus ) ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Omonoid__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(482,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(1597,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Ocancel__ab__semigroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(398,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(1431,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)],[398]) ).

thf(189,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(1004,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)],[189]) ).

thf(436,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(1505,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(494,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(1621,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)],[494]) ).

thf(343,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(1320,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)],[343]) ).

thf(191,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(1009,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)],[191]) ).

thf(287,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(1204,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)],[287]) ).

thf(3551,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_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(paramod_ordered,[status(thm)],[1041,636]) ).

thf(3552,plain,
    ! [A: $i] :
      ( ( ( tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom )
       != ( A @ class_Ring__and__Field_Oordered__idom ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add ) ),
    inference(simp,[status(thm)],[3551]) ).

thf(3553,plain,
    tc_RealDef_Oreal @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__comm__monoid__add,
    inference(pattern_uni,[status(thm)],[3552:[bind(A,$thf( tc_RealDef_Oreal ))]]) ).

thf(128,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).

thf(882,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Omonoid__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(2319,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)],[1874,608]) ).

thf(2320,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)],[2319]) ).

thf(2321,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Omult__zero,
    inference(pattern_uni,[status(thm)],[2320:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly ))]]) ).

thf(510,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

thf(1653,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( D @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(368,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_add__increasing_0) ).

thf(1367,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Ocomm__monoid__add )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__semigroup__add__imp__le ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(159,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(940,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)],[159]) ).

thf(524,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(1681,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)],[524]) ).

thf(276,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(1184,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)],[276]) ).

thf(467,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(1565,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)],[467]) ).

thf(174,axiom,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).

thf(972,plain,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(2851,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( B @ v_x @ ( tc_Complex_Ocomplex @ ( v_cs____ @ ( v_c____ @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ $true ),
    inference(paramod_ordered,[status(thm)],[972,569]) ).

thf(2852,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) )
       != ( tc_RealDef_Oreal @ ( B @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( B @ v_x @ ( tc_Complex_Ocomplex @ ( v_cs____ @ ( v_c____ @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2851]) ).

thf(2865,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal != tc_RealDef_Oreal )
      | ( A != B )
      | ( A
       != ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( B @ v_x @ ( tc_Complex_Ocomplex @ ( v_cs____ @ ( v_c____ @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2852]) ).

thf(2866,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ v_x @ ( tc_Complex_Ocomplex @ ( v_cs____ @ ( v_c____ @ c_Polynomial_OpCons ) ) @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != A )
      | ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
    inference(simp,[status(thm)],[2865]) ).

thf(2830,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(paramod_ordered,[status(thm)],[2480,571]) ).

thf(2831,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add )
       != ( A @ class_OrderedGroup_Oab__group__add ) )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add ) ),
    inference(simp,[status(thm)],[2830]) ).

thf(2832,plain,
    tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_OrderedGroup_Oab__group__add,
    inference(pattern_uni,[status(thm)],[2831:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(75,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).

thf(755,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(46,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
        = ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sgn__times_0) ).

thf(676,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Osgn__class_Osgn ) )
        = ( A @ ( A @ ( C @ c_HOL_Osgn__class_Osgn ) @ ( A @ ( B @ c_HOL_Osgn__class_Osgn ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(230,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( D @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( E @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__mult__less_0) ).

thf(1088,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( D @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( E @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
      | ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(58,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

thf(708,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_HOL_Oplus__class_Oplus ) ) @ c_HOL_Oplus__class_Oplus ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Oplus__class_Oplus ) ) @ ( B @ c_HOL_Oplus__class_Oplus ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(2978,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ~ $true
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(paramod_ordered,[status(thm)],[2535,573]) ).

thf(2979,plain,
    ! [A: $i] :
      ( ( ( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 )
       != ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(simp,[status(thm)],[2978]) ).

thf(2980,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__1,
    inference(pattern_uni,[status(thm)],[2979:[bind(A,$thf( tc_Complex_Ocomplex @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly @ tc_Polynomial_Opoly ))]]) ).

thf(193,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(1014,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)],[193]) ).

thf(392,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(1417,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)],[392]) ).

thf(5807,plain,
    $false,
    inference(e,[status(thm)],[809,2094,629,1469,1995,1105,1729,628,2787,2544,1179,1818,1549,1110,645,892,3021,1322,4447,1718,1369,1190,1168,4005,2336,2131,2480,1083,1982,730,1443,1618,994,1401,1544,1591,1041,1486,1750,977,1158,582,1406,2104,741,1073,878,655,614,1692,1305,597,1705,1608,1655,1137,4011,1735,1867,797,814,1640,1063,4435,1354,670,2476,698,1761,747,1507,930,829,1196,4792,2046,841,1613,4916,1803,1887,651,1243,1782,3249,1441,973,885,1645,1921,1601,1386,1904,1518,1703,1228,1623,1254,2654,1709,570,2039,719,802,1313,4023,1992,1059,1660,1298,3617,1330,587,838,1577,1455,817,1379,1514,1147,870,1479,770,1568,3014,2024,1494,1362,3602,2829,638,853,1247,2049,606,1347,1572,1741,1398,1232,4008,4432,1415,789,591,1373,1632,2650,623,646,834,1864,1677,4396,1465,1302,1664,2794,2324,1714,2027,4072,1450,1020,574,1183,1283,1169,3537,1377,2281,2483,1119,1351,660,998,988,1433,849,1521,1696,602,766,1215,634,2523,1072,2103,1405,1943,1201,1651,1206,942,925,1306,1199,2118,1338,1311,1636,1438,661,1153,761,1067,2790,2660,714,1047,1163,1274,1091,1021,1580,1123,1666,693,1560,1387,910,957,894,825,1343,2560,1042,952,1519,3867,1570,1174,1217,2147,1502,820,2150,1370,1238,2015,3958,1365,2477,2826,3556,1296,1624,2181,1210,682,1128,1291,1740,847,2758,566,3980,1837,1602,1687,1457,583,2200,1079,1027,578,1234,615,1064,2631,1138,1755,989,3018,1360,1936,874,2115,1270,1259,650,948,1534,1017,2841,1328,1375,1121,1970,1227,4789,4048,725,980,1587,1096,1672,1540,1006,1567,1160,1028,1361,4276,933,753,1461,642,637,1214,1446,590,4444,1644,1155,706,884,1329,901,1075,1424,2312,1414,2196,2172,4054,679,1039,970,2781,1419,3242,1263,985,1150,1192,1050,4934,1002,1874,1720,1825,2968,1324,1530,1382,1266,2153,1131,654,3760,569,1429,1979,779,4069,1759,1393,1627,1525,1333,1318,1241,2043,1695,921,657,1026,2189,953,2529,1732,3807,2634,2749,1202,792,2203,1814,938,1712,1054,1286,1035,1515,2221,773,586,1135,2001,1698,3042,1219,1273,2570,1595,573,4365,733,601,2144,906,965,750,1727,618,1764,4919,1146,1754,904,1615,2657,1752,1388,579,1701,1520,2134,584,4943,843,1125,577,711,1226,1488,641,1669,936,572,1707,1271,611,1239,1090,1464,3568,1675,1635,1733,2055,1092,1897,919,804,1638,1224,2573,1356,2346,831,1408,1282,1894,784,1011,736,1349,1542,567,1690,1307,863,764,604,1589,996,2284,1933,1492,1603,1722,1144,880,649,599,1439,890,811,631,858,1630,2780,621,700,3614,626,1344,1556,2974,1061,1877,1471,758,3027,2343,2625,609,2111,1731,594,799,3932,1293,2553,983,1474,959,1528,883,1113,1477,2535,1102,2156,653,922,1973,658,1562,912,685,768,827,2835,636,695,1245,1176,608,1775,1000,1435,1364,1250,1496,2303,2005,722,1034,4907,1662,944,1467,927,1684,648,1509,1081,617,2333,968,3571,1049,1758,1166,1203,1208,589,795,2318,1277,2124,836,1551,4045,4937,1743,887,739,1098,2567,1845,1547,776,1748,580,855,1516,1598,1070,872,2143,2012,1605,2588,4922,1647,954,1252,1230,1484,673,1790,2165,4020,4768,2128,1317,3544,1679,1738,907,1711,3080,1053,1499,1300,1452,1188,1186,1038,585,1085,576,1658,1538,2486,1336,643,744,1257,703,1221,600,1052,1427,727,571,595,876,991,1404,1358,1141,2992,1536,656,1023,1585,1094,1670,1797,3024,1717,2030,1881,612,1940,845,1421,627,3565,1459,1180,931,1553,4165,581,1412,1517,2209,1126,1289,1918,1316,1649,4419,1834,976,688,1448,1189,1390,1575,1108,3039,1326,961,963,1476,2290,1481,4042,1745,1523,786,781,2526,1558,588,4913,1341,896,946,1101,632,2971,1861,1689,568,914,4214,2330,2576,1193,1212,1607,899,1309,1442,1045,1030,1491,667,4774,2462,1077,2162,716,1614,1116,1133,1642,1512,950,1546,1986,1248,865,603,2287,620,1725,1280,1395,1625,1593,1380,1527,1673,867,4357,807,2091,1891,3030,2040,2340,3045,2651,918,1989,4051,1172,897,1410,1056,664,1033,1710,635,1473,2021,1346,1610,1742,928,624,1236,2159,1129,1261,1152,596,1582,4066,908,1500,822,691,607,1268,575,1532,860,1384,3605,1976,644,3939,850,1597,1431,1004,1505,1621,1320,1009,2206,1848,639,1204,3553,592,882,2321,1653,1367,940,1681,1184,1463,1565,2018,2866,2832,1490,1037,2297,755,676,2351,1088,708,2980,1014,1417,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03  % Problem  : ALG342-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07  % 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
% 0.13/0.39  % Computer : n014.cluster.edu
% 0.13/0.39  % Model    : x86_64 x86_64
% 0.13/0.39  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.39  % Memory   : 8046.5625MB
% 0.13/0.39  % OS       : Linux 6.8.0-71-generic
% 0.13/0.39  % CPULimit : 300
% 0.13/0.39  % WCLimit  : 300
% 0.13/0.39  % DateTime : Sat Sep 26 21:53:16 UTC 2026
% 0.13/0.39  % CPUTime  : 
% 0.13/0.39  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
% 1.26/1.19  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 3.05/1.77  % [INFO] 	 Parsing done (568ms). 
% 3.05/1.79  % [INFO] 	 Running in sequential loop mode. 
% 4.70/2.41  % [INFO] 	 eprover registered as external prover. 
% 4.70/2.42  % [INFO] 	 Scanning for conjecture ... 
% 5.53/2.70  % [INFO] 	 Found a conjecture (or negated_conjecture) and 563 axioms. Running axiom selection ... 
% 6.43/3.02  % [INFO] 	 Axiom selection finished. Selected 563 axioms (removed 0 axioms). 
% 8.47/3.47  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 8.78/3.52  % [INFO] 	 Type checking passed. 
% 8.78/3.53  % [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 ... 
% 104.09/24.64  % External prover 'e' found a proof!
% 104.09/24.64  % [INFO] 	 Killing All external provers ... 
% 104.09/24.65  % Time passed: 24045ms (effective reasoning time: 22847ms)
% 104.09/24.66  % Axioms used in derivation (563): cls_mult__less__cancel__left__disj_5, cls_add__0__left_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_add__pos__nonneg_0, 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_mult__zero__right_0, cls_less__divide__eq_3, clsarity_Polynomial__Opoly__Ring__and__Field_Oidom, cls_le__divide__eq_8, cls_order__le__less__trans_0, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__comm__monoid__add, cls_divide__le__eq_2, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_divide__less__0__iff_0, cls_comm__semiring__class_Odistrib_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_real__mult__le__cancel__iff1_0, cls_divide__pos__pos_0, cls_mult__imp__le__div__pos_0, clsarity_RealDef__Oreal__Orderings_Opreorder, cls_class__ringb_Oadd__r0__iff_1, cls_mult__nonneg__nonneg_0, clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one, cls_add__less__cancel__left_1, cls_mult__right__mono_0, cls_mult__right_Ozero_0, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_zero__less__divide__iff_5, cls_xt1_I12_J_0, cls_mult__less__cancel__right__disj_0, cls_mult__nonneg__nonpos2_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_sgn__times_0, cls_real__mult__le__cancel__iff2_1, cls_mult__less__cancel__left__disj_1, cls_norm__zero_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, clsarity_Polynomial__Opoly__Orderings_Olinorder, cls_real__mult__assoc_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors, cls_real__less__def_1, cls_sum__squares__eq__zero__iff_0, cls_zero__less__norm__iff_1, cls_divide__nonpos__neg_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_add__increasing2_0, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1, cls_pCons_Ohyps_1, cls_zero__le__mult__iff_3, clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__mult, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring, cls_CHAINED_0, cls_not__sum__squares__lt__zero_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_pos__add__strict_0, cls_zero__le__divide__iff_2, cls_linorder__neqE_0, cls_add__strict__right__mono_0, cls_power__le__zero__eq_3, cls_class__semiring_Osemiring__rules_I21_J_0, cls_sgn0_0, cls_divide__less__eq_4, cls_zero__less__divide__iff_0, cls_Rational_Oordered__idom__class_Osgn__greater_1, clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add, cls_class__semiring_Osemiring__rules_I10_J_0, cls_add__imp__eq_0, cls_divide__le__eq_7, cls_frac__le_0, cls_add__le__cancel__right_1, cls_add__le__cancel__left_1, cls_divide__le__eq_8, cls_real__le__trans_0, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add, cls_real__mult__less__iff1_0, clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__1__no__zero__divisors, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field, clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add, cls_mult__nonpos__nonneg_0, cls_power__less__zero__eq_1, cls_divide__eq__eq_0, cls_mult__nonpos__nonpos_0, cls_class__ringb_Onoteq__reduce_0, cls_comm__monoid__add_Omult__1__right_0, cls_sum__squares__ge__zero_0, cls_add__nonpos__neg_0, cls_mult__less__imp__less__right_0, cls_comm__monoid__add_Omult__assoc_0, cls_order__less__trans_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_divide__less__eq_5, cls_add__cancel__21_1, cls_real__mult__le__cancel__iff2_0, cls_add__left__cancel_0, 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_sum__squares__le__zero__iff_1, cls_sgn__zero_0, cls_less__divide__eq_4, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult, cls_mult__eq__0__iff_0, cls_add__nonneg__pos_0, cls_divide__strict__left__mono_0, cls_mult__less__cancel__left__disj_4, cls_class__ringb_Oadd__mul__solve_1, cls_mult__less__cancel__right__disj_3, clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_frac__eq__eq_0, cls_divide__eq__eq_4, clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__add, cls_mult__left__mono__neg_0, cls_add__right__mono_0, cls_mult_Ozero__left_0, cls_divide__neg__neg_0, cls_eq__divide__eq_4, cls_mult__mono_0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_class__semiring_Omul__0_0, cls_field__power__not__zero_0, cls_order__less__asym_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_linorder__not__less_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_zero__le__mult__iff_0, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_order__le__less_0, cls_double__eq__0__iff_1, clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra, cls_real__le__linear_0, cls_mult__strict__right__mono_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors, cls_class__semiring_Omul__c_0, cls_mult__pos__neg_0, cls_order__eq__refl_0, 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__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_mult_Oadd__left_0, cls_linorder__antisym__conv2_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semidom, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__semigroup__add, cls_mult__right_Oadd_0, cls_divide__left__mono__neg_0, cls_real__less__def_0, cls_less__divide__eq_7, cls_le__divide__eq_7, cls_divide__right__mono_0, cls_divide__right__mono__neg_0, cls_xt1_I10_J_0, cls_add__nonneg__eq__0__iff_0, cls_le__divide__eq_2, cls_add__divide__distrib_0, cls_divide__le__eq_3, cls_not__less__iff__gr__or__eq_0, 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_zero__le__double__add__iff__zero__le__single__add_1, clsarity_Polynomial__Opoly__HOL_Ozero, cls_less__le__not__le_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_divide__neg__pos_0, clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero, cls_add__left__mono_0, cls_norm__ge__zero_0, cls_add__less__cancel__right_1, cls_divide__less__eq_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_norm__sgn_0, cls_CHAINED_0_01, cls_add__strict__left__mono_0, cls_sgn__0__0_0, cls_less__divide__eq_2, cls_Rational_Oordered__idom__class_Osgn__less_0, cls_ln__less__cancel__iff_1, cls_real__le__refl_0, cls_mult__neg__pos_0, cls_norm__not__less__zero_0, cls_combine__common__factor_0, cls_zero__less__divide__iff_1, clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult, cls_mult__frac__frac_0, cls_mult__le__0__iff_0, cls_add__le__less__mono_0, cls_mult__right__le__imp__le_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring, cls_pCons__eq__iff_0, cls_zero__le__divide__iff_3, cls_pos__poly__pCons_2, cls_class__ringb_Onoteq__reduce_1, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add, cls_sgn__0__0_1, cls_real__mult__less__mono2_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add, cls_mult__pos__neg2_0, 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_class__semiring_Oadd__a_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_class__semiring_Osemiring__rules_I19_J_0, cls_xt1_I8_J_0, cls_eq__divide__eq_0, clsarity_Polynomial__Opoly__OrderedGroup_Ocomm__monoid__add, cls_mult__le__cancel__left__neg_1, cls_eq__divide__eq_3, cls_class__semiring_Oadd__0_0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_mult__left__idem_0, cls_add__right__cancel_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__1, cls_mult__le__cancel__left__pos_1, cls_mult__le__0__iff_1, cls_zero__less__mult__pos_0, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add, cls_class__semiring_Osemiring__rules_I1_J_0, cls_split__mult__pos__le_0, cls_sum__squares__le__zero__iff_2, cls_divide_Ozero_0, cls_divide__self__if_0, cls_zero__le__power__iff_1, cls_class__semiring_Osemiring__rules_I17_J_0, cls_mult__imp__div__pos__le_0, cls_poly__pCons_0, cls_comm__monoid__add_Omult__commute_0, clsarity_RealDef__Oreal__Power_Opower, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add, cls_mult__le__0__iff_4, cls_linorder__linear_0, cls_real__mult__less__iff1_1, clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict, cls_class__ringb_Oadd__mul__solve_0, cls_add__strict__mono_0, cls_sum__squares__eq__zero__iff_1, cls_zero__le__divide__iff_5, cls_divide__less__0__iff_3, 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_zero__less__power_0, cls_sgn__zero__iff_0, cls_add__cancel__21_0, cls_order__trans_0, cls_divide__nonneg__neg_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, cls_power__divide_0, cls_mult__strict__left__mono_0, cls_sum__squares__gt__zero__iff_2, cls_divide__le__0__iff_2, cls_class__semiring_Omul__d_0, cls_real__mult__order_0, cls_order__antisym_0, cls_divide__le__eq_6, cls_divide__less__eq_1, cls_mult__left__less__imp__less_0, cls_linorder__antisym__conv1_1, cls_real__gt__zero__preal__Ex_1, cls_real__mult__left__cancel_0, cls_add__frac__eq_0, cls_no__zero__divirors__neq0_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict, cls_mult__le__0__iff_5, clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add, cls_add__num__frac_0, cls_mult__strict__mono_H_0, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_less__divide__eq_5, cls_ln__less__cancel__iff_0, cls_class__semiring_Osemiring__rules_I5_J_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ozero__neq__one, clsarity_Polynomial__Opoly__Power_Opower, cls_split__mult__pos__le_1, cls_less__divide__eq_8, cls_divide__le__eq_0, cls_zero__less__divide__iff_3, clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector, cls_ln__less__self_0, cls_zero__le__divide__iff_4, cls_real__mult__right__cancel_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add, cls_Rational_Oordered__idom__class_Osgn__less_1, clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add, cls_divide__nonneg__pos_0, cls_mult__less__cancel__right__disj_5, clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one, cls_real__less__all__preal_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__comm__monoid__add, clsarity_RealDef__Oreal__HOL_Ozero, cls_divide__le__0__iff_5, cls_linorder__not__le_1, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring, clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult, cls_add__less__cancel__right_0, cls_divide__zero_0, 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_zero__less__double__add__iff__zero__less__single__add_1, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_add__increasing_0, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero, cls_m_0, cls_class__ringb_Oadd__scale__eq__noteq_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oidom, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add, cls_order__le__neq__trans_0, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring, cls_real__of__preal__zero__less_0, cls_mult__nonneg__nonpos_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_less__divide__eq_1, cls_zero__less__divide__iff_2, cls_pCons_0, clsarity_RealDef__Oreal__Ring__and__Field_Oidom, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_le__divide__eq_6, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1, cls_class__ringb_Oadd__cancel_0, cls_add__nonpos__nonpos_0, cls_divide__pos__neg_0, cls_less__le__not__le_1, clsarity_Polynomial__Opoly__Ring__and__Field_Osemiring, cls_add__nonneg__eq__0__iff_1, cls_le__divide__eq_1, cls_divide__le__0__iff_1, 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clsarity_RealDef__Oreal__Ring__and__Field_Ofield, clsarity_Polynomial__Opoly__OrderedGroup_Ocancel__comm__monoid__add, cls_order__less__le_2, cls_divide__strict__right__mono__neg_0, cls_mult__less__cancel__left__pos_1, cls_zero__le__mult__iff_5, cls_divide__le__eq_5, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0, cls_ln__inj__iff_0, cls_zero__le__mult__iff_1, cls_power__commutes_0, cls_xt1_I11_J_0, cls_add__neg__neg_0, cls_mult__imp__div__pos__less_0, cls_double__eq__0__iff_0, cls_mult__le__0__iff_2, cls_norm__mult_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__field, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector, cls_divide__eq__imp_0, cls_mult__le__cancel__left__neg_0, cls_divide__less__eq_7, cls_zero__le__divide__iff_0, cls_norm__eq__zero_0, cls_class__semiring_Osemiring__rules_I18_J_0, cls_sum__squares__eq__zero__iff_2, cls_real__le__antisym_0, cls_divide__less__0__iff_2, cls_xt1_I6_J_0, cls_le__add__right__mono_0, cls_zero__less__mult__pos2_0, 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clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring, cls_divide__less__eq_6, cls_class__semiring_Osemiring__rules_I25_J_0, clsarity_Polynomial__Opoly__Ring__and__Field_Osgn__if, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring, cls_mult__eq__0__iff_1, cls_zero__le__power_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, cls_less__divide__eq_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring, cls_order__less__imp__le_0, cls_real__less__def_2, cls_not__real__square__gt__zero_0, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add, cls_divide__nonpos__pos_0, cls_add__less__le__mono_0, clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add, cls_norm__le__zero__iff_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom, cls_divide__less__eq_3, cls_zero__le__divide__iff_1, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__comm__monoid__add, cls_zero__less__norm__iff_0, cls_monoid__add__class_Oadd__0__right_0, cls_mult__idem_0, cls_add__strict__increasing2_0, clsarity_RealDef__Oreal__Int_Onumber__ring, clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if, 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_xt1_I7_J_0, cls_mult__less__le__imp__less_0, clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors, cls_mult__divide__mult__cancel__left_0, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, cls_ln__le__cancel__iff_1, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1, cls_less__divide__eq_9, 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_add__le__cancel__left_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring, cls_even__less__0__iff_0, cls_mult__left_Oadd_0, cls_sum__squares__le__zero__iff_0, cls_add__le__cancel__right_0, cls_mult__less__cancel__left__pos_0, cls_divide__less__0__iff_4, cls_split__mult__neg__le_1, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict, cls_power__mono_0, cls_zero__le__mult__iff_2, cls_divide__le__eq_1, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__strict__left__mono__neg_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, clsarity_Complex__Ocomplex__HOL_Ozero, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors, cls_class__semiring_Osemiring__rules_I22_J_0
% 104.09/24.66  % No. of inferences in proof: 1862
% 104.09/24.66  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 24045 ms resp. 22847 ms w/o parsing
% 107.72/25.29  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 108.32/25.31  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------