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

%------------------------------------------------------------------------------
% File     : Leo-III---1.8.0
% Problem  : ALG373-1 : 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 : n009.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 06:46:46 AM UTC 2026

% Result   : Unsatisfiable 31.96s 8.48s
% Output   : Refutation 32.14s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  485
% Syntax   : Number of formulae    :  971 ( 235 unt;   0 typ;   0 def)
%            Number of atoms       : 2383 ( 356 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 11022 (1332   ~;1412   |;   0   &;8278   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    0 (   0   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   84 (  82 usr;   6 con; 0-3 aty)
%            Number of variables   : 2030 (   0   ^;2030   !;   0   ?;2030   :)

% 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_xa_decl,type,
    v_xa: $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_Polynomial_Opoly_decl,type,
    c_Polynomial_Opoly: $i > $i > $i > $i ).

thf(v_p_decl,type,
    v_p: $i ).

thf(c_HOL_Ouminus__class_Ouminus_decl,type,
    c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).

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

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

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

thf(tc_Int_Oint_decl,type,
    tc_Int_Oint: $i ).

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

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

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

thf(class_Ring__and__Field_Opordered__ring__abs_decl,type,
    class_Ring__and__Field_Opordered__ring__abs: $i > $o ).

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

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

thf(class_OrderedGroup_Oordered__ab__group__add_decl,type,
    class_OrderedGroup_Oordered__ab__group__add: $i > $o ).

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

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

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

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

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

thf(class_OrderedGroup_Opordered__ab__group__add__abs_decl,type,
    class_OrderedGroup_Opordered__ab__group__add__abs: $i > $o ).

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

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

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

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

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

thf(c_RealVector_OscaleR__class_OscaleR_decl,type,
    c_RealVector_OscaleR__class_OscaleR: $i > $i > $i > $i ).

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

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

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

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

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

thf(class_RealVector_Oreal__vector_decl,type,
    class_RealVector_Oreal__vector: $i > $o ).

thf(class_Ring__and__Field_Olordered__ring_decl,type,
    class_Ring__and__Field_Olordered__ring: $i > $o ).

thf(class_RealVector_Oreal__algebra_decl,type,
    class_RealVector_Oreal__algebra: $i > $o ).

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

thf(class_RealVector_Oreal__algebra__1_decl,type,
    class_RealVector_Oreal__algebra__1: $i > $o ).

thf(c_RealVector_Oof__real_decl,type,
    c_RealVector_Oof__real: $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

thf(class_OrderedGroup_Olordered__ab__group__add__abs_decl,type,
    class_OrderedGroup_Olordered__ab__group__add__abs: $i > $o ).

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

thf(c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1_decl,type,
    c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1: $i > $i > $i ).

thf(c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1_decl,type,
    c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1: $i > $i > $i ).

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

thf(c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1_decl,type,
    c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1: $i > $i > $i ).

thf(c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1_decl,type,
    c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1: $i > $i > $i ).

thf(c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1_decl,type,
    c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1: $i > $i > $i ).

thf(c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1_decl,type,
    c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1: $i > $i > $i ).

thf(class_Lattices_Oboolean__algebra_decl,type,
    class_Lattices_Oboolean__algebra: $i > $o ).

thf(v_sko__local__Xmth1__2_decl,type,
    v_sko__local__Xmth1__2: $i > $i > $i ).

thf(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1_decl,type,
    v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1: $i > $i > $i ).

thf(c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1_decl,type,
    c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1: $i > $i > $i ).

thf(v_sko__local__Xmth1__1_decl,type,
    v_sko__local__Xmth1__1: $i > $i > $i ).

thf(c_RealVector_Osko__RealVector__XscaleR__right__Xbounded__1__1_decl,type,
    c_RealVector_Osko__RealVector__XscaleR__right__Xbounded__1__1: $i > $i > $i > $i ).

thf(c_Complex_ORe_decl,type,
    c_Complex_ORe: $i > $i ).

thf(c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1_decl,type,
    c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1: $i > $i > $i ).

thf(c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1_decl,type,
    c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1: $i > $i > $i > $i ).

thf(c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1_decl,type,
    c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1: $i > $i > $i > $i ).

thf(v_sko__unknown__thm__rW8__1_decl,type,
    v_sko__unknown__thm__rW8__1: $i > $i > $i ).

thf(c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1_decl,type,
    c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1: $i > $i > $i ).

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

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

thf(406,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(1322,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)],[406]) ).

thf(264,axiom,
    tc_Complex_Ocomplex @ class_Int_Onumber__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

thf(1036,plain,
    tc_Complex_Ocomplex @ class_Int_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(155,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(809,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)],[155]) ).

thf(476,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(1469,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)],[476]) ).

thf(469,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(1454,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)],[469]) ).

thf(174,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).

thf(846,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(73,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(628,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)],[73]) ).

thf(198,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( D @ c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1 ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ 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_mult_Obounded_0) ).

thf(893,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( D @ c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1 ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ 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)],[198]) ).

thf(285,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).

thf(1083,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(332,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_Oof__real ) )
        = ( A @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__minus_0) ).

thf(1179,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_Oof__real ) )
        = ( A @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(298,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1 ) @ ( 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_mult__left_Obounded_0) ).

thf(1110,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1 ) @ ( 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)],[298]) ).

thf(81,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(645,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)],[81]) ).

thf(197,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(892,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__ring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(326,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(1168,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)],[326]) ).

thf(131,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(760,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)],[131]) ).

thf(403,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).

thf(1315,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(26,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_OscaleR_0) ).

thf(518,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(28,axiom,
    tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult) ).

thf(523,plain,
    tc_Int_Oint @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(448,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(1406,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)],[448]) ).

thf(389,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).

thf(1290,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(463,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_Complex_Ocomplex @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( C @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__bound__exists_1) ).

thf(1443,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( C @ ( tc_Complex_Ocomplex @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( C @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( B @ ( A @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(454,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(1422,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)],[454]) ).

thf(281,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__scaleR_0) ).

thf(1073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(344,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(1205,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)],[344]) ).

thf(94,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Omult__mono,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono) ).

thf(677,plain,
    tc_Int_Oint @ class_Ring__and__Field_Omult__mono,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(461,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ominus__right_0) ).

thf(1437,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(183,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(861,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)],[183]) ).

thf(329,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(1173,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)],[329]) ).

thf(190,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(878,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(23,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(511,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)],[23]) ).

thf(400,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(1310,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)],[400]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_OscaleR__left_0) ).

thf(550,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(13,axiom,
    tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add) ).

thf(500,plain,
    tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(357,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 ) @ ( 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_mult__left_Ononneg__bounded_1) ).

thf(1233,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 ) @ ( 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)],[357]) ).

thf(105,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(698,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)],[105]) ).

thf(415,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(1342,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)],[415]) ).

thf(222,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__algebra__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).

thf(945,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__algebra__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(277,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(1063,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)],[277]) ).

thf(215,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).

thf(930,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(471,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).

thf(1458,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(324,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Ogroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).

thf(1164,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Ogroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(149,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Oof__real ) )
        = ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__mult_0) ).

thf(797,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_Oof__real ) )
        = ( A @ ( A @ ( C @ c_RealVector_Oof__real ) @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(37,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(538,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)],[37]) ).

thf(421,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(1354,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)],[421]) ).

thf(165,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Opos__bounded_0) ).

thf(829,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(200,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).

thf(898,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(247,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).

thf(1001,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(439,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(1391,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)],[439]) ).

thf(142,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ( A
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rabs__ratiotest__lemma_0) ).

thf(782,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ( A
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(436,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(1386,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(479,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(1475,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)],[479]) ).

thf(47,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict) ).

thf(565,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(375,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oabs__if,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).

thf(1265,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oabs__if,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(483,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).

thf(1482,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(193,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(885,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)],[193]) ).

thf(269,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__number__of_0) ).

thf(1046,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(449,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 ) ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_0) ).

thf(1409,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 ) ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(50,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Omult__mono1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__mono1) ).

thf(570,plain,
    tc_Int_Oint @ class_Ring__and__Field_Omult__mono1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(457,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 ) @ ( A @ ( C @ 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_mult__right_Opos__bounded_1) ).

thf(1430,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 ) @ ( A @ ( C @ 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)],[457]) ).

thf(394,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(1298,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)],[394]) ).

thf(114,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add) ).

thf(719,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(143,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ononneg__bounded_0) ).

thf(785,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(17,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring) ).

thf(504,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(151,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Opos__bounded_0) ).

thf(802,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(383,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 ) @ ( A @ ( C @ 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_mult__right_Ononneg__bounded_1) ).

thf(1279,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 ) @ ( A @ ( C @ 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)],[383]) ).

thf(225,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).

thf(949,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(209,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(917,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)],[209]) ).

thf(107,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(702,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)],[107]) ).

thf(127,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).

thf(751,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(217,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(934,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)],[217]) ).

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

thf(1191,plain,
    tc_RealDef_Oreal @ class_Int_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

thf(159,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( D @ c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ 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_mult_Ononneg__bounded_1) ).

thf(817,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( D @ c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ 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)],[159]) ).

thf(287,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__algebra__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).

thf(1087,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__algebra__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(316,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(1147,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(364,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(1247,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)],[364]) ).

thf(187,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).

thf(870,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(481,axiom,
    ! [A: $i] :
      ( ~ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).

thf(1479,plain,
    ! [A: $i] :
      ( ~ ( A @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(425,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(1362,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)],[425]) ).

thf(77,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(638,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)],[77]) ).

thf(178,axiom,
    tc_RealDef_Oreal @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).

thf(853,plain,
    tc_RealDef_Oreal @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(234,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(969,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)],[234]) ).

thf(418,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(1347,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)],[418]) ).

thf(451,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(1415,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)],[451]) ).

thf(5,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring) ).

thf(492,plain,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(59,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber__ring) ).

thf(591,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(266,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(1040,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)],[266]) ).

thf(71,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(623,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)],[71]) ).

thf(24,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(514,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)],[24]) ).

thf(52,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(574,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)],[52]) ).

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(806,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(232,axiom,
    tc_RealDef_Oreal @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Oring__char__0) ).

thf(966,plain,
    tc_RealDef_Oreal @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(385,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(1283,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)],[385]) ).

thf(203,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(905,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)],[203]) ).

thf(396,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( D @ c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1 ) ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Opos__bounded_1) ).

thf(1302,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( D @ c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1 ) ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(129,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(756,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)],[129]) ).

thf(311,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(1136,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)],[311]) ).

thf(168,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra) ).

thf(834,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(133,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(766,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)],[133]) ).

thf(99,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(687,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)],[99]) ).

thf(432,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).

thf(1377,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(102,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(692,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)],[102]) ).

thf(120,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).

thf(734,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(185,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(866,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)],[185]) ).

thf(441,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__leI_0) ).

thf(1394,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(420,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(1351,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)],[420]) ).

thf(87,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(660,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)],[87]) ).

thf(447,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(1405,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(342,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(1201,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)],[342]) ).

thf(20,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__ring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict) ).

thf(507,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__ring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(30,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__ring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1) ).

thf(527,plain,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__ring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(303,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ 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_less__minus__self__iff_0) ).

thf(1119,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ 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)],[303]) ).

thf(137,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).

thf(774,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(417,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).

thf(1345,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(242,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(988,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)],[242]) ).

thf(211,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = B )
      | ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).

thf(920,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = B )
      | ( ( A @ c_HOL_Ozero__class_Ozero )
       != ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(220,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 ) @ ( 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_mult__left_Opos__bounded_1) ).

thf(942,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 ) @ ( 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)],[220]) ).

thf(95,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(678,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)],[95]) ).

thf(32,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__0) ).

thf(529,plain,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(147,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).

thf(793,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(213,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(925,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)],[213]) ).

thf(398,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(1306,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)],[398]) ).

thf(341,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(1199,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)],[341]) ).

thf(413,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ 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_minus__le__self__iff_0) ).

thf(1338,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ 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)],[413]) ).

thf(35,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
       != ( A @ ( C @ ( D @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__right_0) ).

thf(534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( B = D )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
       != ( A @ ( C @ ( D @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(112,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(714,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)],[112]) ).

thf(273,axiom,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ ( A @ c_Complex_ORe @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__Re__le__cmod_0) ).

thf(1057,plain,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ ( A @ c_Complex_ORe @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(380,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(1274,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)],[380]) ).

thf(353,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(1223,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)],[353]) ).

thf(289,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).

thf(1091,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(163,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(825,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)],[163]) ).

thf(370,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(1255,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)],[370]) ).

thf(161,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_1) ).

thf(820,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(45,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Oab__group__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add) ).

thf(561,plain,
    ! [A: $i] :
      ( ~ ( A @ class_OrderedGroup_Oab__group__add )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(485,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ozero__left_0) ).

thf(1487,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(74,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(630,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)],[74]) ).

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_Oorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(1370,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)],[429]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Int_Oring__char__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__number__of_0) ).

thf(729,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) )
       != ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Int_Oring__char__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(360,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

thf(1238,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(437,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

thf(1387,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(205,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(910,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)],[205]) ).

thf(255,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(1021,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)],[255]) ).

thf(139,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).

thf(778,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(267,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( D @ c_RealVector_Osko__RealVector__XscaleR__right__Xbounded__1__1 ) ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Obounded_0) ).

thf(1042,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( D @ c_RealVector_Osko__RealVector__XscaleR__right__Xbounded__1__1 ) ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(227,axiom,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) )
        = A ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__abs__def_1) ).

thf(952,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) )
        = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(350,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__interval__iff_1) ).

thf(1217,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_OscaleR_0) ).

thf(598,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(208,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

thf(916,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(48,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oabs__if,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oabs__if) ).

thf(566,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oabs__if,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(261,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).

thf(1032,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( D @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( E @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(427,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(1365,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)],[427]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_OscaleR__right_0) ).

thf(625,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).

thf(879,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(177,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Olordered__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) ).

thf(852,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Olordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(55,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring) ).

thf(583,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(195,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(889,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)],[195]) ).

thf(322,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ 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_le__minus__self__iff_0) ).

thf(1159,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ 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)],[322]) ).

thf(283,axiom,
    tc_Complex_Ocomplex @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Oring__char__0) ).

thf(1079,plain,
    tc_Complex_Ocomplex @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(307,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != B )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).

thf(1128,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != B )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(384,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).

thf(1281,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(390,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(1291,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Oorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(172,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).

thf(842,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(236,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(974,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( B @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(296,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(1106,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)],[296]) ).

thf(392,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

thf(1296,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__vector,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(89,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult_0) ).

thf(665,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(6,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict) ).

thf(493,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(346,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).

thf(1210,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(97,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(682,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)],[97]) ).

thf(339,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(1195,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)],[339]) ).

thf(446,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).

thf(1402,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(424,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( D @ c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ 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_mult_Opos__bounded_1) ).

thf(1360,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( D @ c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 ) @ ( tc_RealDef_Oreal @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ 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)],[424]) ).

thf(123,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(742,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)],[123]) ).

thf(104,axiom,
    tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add__abs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs) ).

thf(697,plain,
    tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(83,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(650,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)],[83]) ).

thf(253,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__ring__abs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) ).

thf(1017,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__ring__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(68,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(615,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)],[68]) ).

thf(304,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(1121,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( D @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__vector_Oscale__scale_0) ).

thf(980,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( D @ ( tc_RealDef_Oreal @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(455,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 ) ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_3) ).

thf(1425,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 ) ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(291,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(1096,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)],[291]) ).

thf(249,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(1006,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)],[249]) ).

thf(60,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0) ).

thf(593,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__semiring__0 )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__semiring__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(186,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(869,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(66,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__scaleR__left_0) ).

thf(610,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(302,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(1118,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(12,axiom,
    tc_Int_Oint @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Opreorder) ).

thf(499,plain,
    tc_Int_Oint @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(443,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(1397,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)],[443]) ).

thf(378,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(1270,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)],[378]) ).

thf(372,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__left_1) ).

thf(1259,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( C @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(409,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).

thf(1329,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(259,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).

thf(1028,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(3,negated_conjecture,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( A @ ( A @ v_x @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(488,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( A @ ( A @ v_x @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(128,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( B
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
       != ( A @ ( D @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__left_0) ).

thf(753,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( C = D )
      | ( B
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
       != ( A @ ( D @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(333,axiom,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ ( v_r @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_p @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_p @ v_sko__unknown__thm__rW8__1 ) @ ( v_p @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_calculation_0) ).

thf(1182,plain,
    ! [A: $i] :
      ( ( tc_RealDef_Oreal @ ( v_r @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_p @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_p @ v_sko__unknown__thm__rW8__1 ) @ ( v_p @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(91,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__cancel__right_1) ).

thf(669,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).

thf(901,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(348,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).

thf(1214,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(109,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(706,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)],[109]) ).

thf(453,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 @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_1) ).

thf(1419,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 @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(472,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).

thf(1461,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(36,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Olordered__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Olordered__ring) ).

thf(537,plain,
    tc_Int_Oint @ class_Ring__and__Field_Olordered__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(320,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(1155,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(40,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( C @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__conv__of__real_0) ).

thf(547,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( C @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(170,axiom,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).

thf(837,plain,
    ! [A: $i] :
      ( ( ( A @ c_HOL_Ozero__class_Ozero )
        = ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(374,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( C @ ( B @ c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1 ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Ononneg__bounded_0) ).

thf(1263,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( C @ ( B @ c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1 ) ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(293,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).

thf(1099,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(106,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Omult__zero,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Omult__zero) ).

thf(701,plain,
    tc_Int_Oint @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(393,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(1297,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__div__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(467,axiom,
    tc_Complex_Ocomplex @ class_Int_Onumber,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber) ).

thf(1451,plain,
    tc_Complex_Ocomplex @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(308,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(1131,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)],[308]) ).

thf(338,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__left_Ominus_0) ).

thf(1192,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(275,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(1060,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)],[275]) ).

thf(115,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs) ).

thf(721,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(140,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(779,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)],[140]) ).

thf(407,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(1324,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)],[407]) ).

thf(300,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(1114,plain,
    ! [A: $i] :
      ~ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(318,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(1150,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)],[318]) ).

thf(365,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring) ).

thf(1249,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(470,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(1456,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)],[470]) ).

thf(434,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(1382,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)],[434]) ).

thf(376,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(1266,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)],[376]) ).

thf(356,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1 ) @ ( A @ ( C @ 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_mult__right_Obounded_0) ).

thf(1231,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1 ) @ ( A @ ( C @ 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)],[356]) ).

thf(16,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oidom) ).

thf(503,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(440,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).

thf(1393,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Ogroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(411,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(1333,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)],[411]) ).

thf(459,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(1434,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)],[459]) ).

thf(404,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__interval__iff_2) ).

thf(1318,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( tc_RealDef_Oreal @ ( B @ ( A @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(286,axiom,
    tc_RealDef_Oreal @ class_Orderings_Opreorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).

thf(1086,plain,
    tc_RealDef_Oreal @ class_Orderings_Opreorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(362,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(1241,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)],[362]) ).

thf(75,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(633,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)],[75]) ).

thf(21,axiom,
    tc_Int_Oint @ class_Orderings_Oorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Oorder) ).

thf(508,plain,
    tc_Int_Oint @ class_Orderings_Oorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(38,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__scaleR__right_0) ).

thf(541,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(272,axiom,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_0) ).

thf(1054,plain,
    ! [B: $i,A: $i] :
      ( ( A
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(327,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(1170,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)],[327]) ).

thf(93,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(674,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)],[93]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).

thf(1026,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_Int_Onumber__class_Onumber__of ) @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_lessequals ) ) )
      | ~ ( A @ class_Int_Onumber )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(33,axiom,
    tc_Int_Oint @ class_Int_Onumber,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber) ).

thf(530,plain,
    tc_Int_Oint @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(88,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__left__commute_0) ).

thf(662,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(387,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(1286,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)],[387]) ).

thf(263,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

thf(1035,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(474,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(1466,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)],[474]) ).

thf(44,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(558,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)],[44]) ).

thf(280,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(1071,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)],[280]) ).

thf(136,axiom,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).

thf(773,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oidom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(57,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(586,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)],[57]) ).

thf(310,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__group__add__abs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).

thf(1135,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Opordered__ab__group__add__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(295,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__number__of_1) ).

thf(1103,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_Int_Onumber__class_Onumber__of ) ) )
      | ~ ( A @ class_Int_Onumber__ring )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(351,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(1219,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)],[351]) ).

thf(125,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(745,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)],[125]) ).

thf(100,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oring) ).

thf(689,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(431,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(1374,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)],[431]) ).

thf(63,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(601,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( E @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) @ ( D @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(367,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(1251,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(69,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(618,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)],[69]) ).

thf(56,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Onumber) ).

thf(584,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring__1 )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Onumber ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

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

thf(819,plain,
    tc_RealDef_Oreal @ class_Int_Onumber,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(119,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__ring__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs) ).

thf(732,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Opordered__ring__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(306,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(1125,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)],[306]) ).

thf(438,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Oabs__if ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_1) ).

thf(1388,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = B )
      | ~ ( A @ class_Ring__and__Field_Oabs__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).

thf(958,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(354,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).

thf(1226,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(189,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).

thf(875,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(53,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(577,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)],[53]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_OscaleR__right_0) ).

thf(711,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( D @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( D @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ ( C @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(456,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).

thf(1428,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(312,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(1139,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)],[312]) ).

thf(218,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).

thf(936,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add__abs )
      | ~ ( A @ class_Orderings_Olinorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(401,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).

thf(1312,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(144,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_p @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).

thf(787,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Oone__class_Oone @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ ( v_p @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
       != ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(11,axiom,
    tc_Int_Oint @ class_OrderedGroup_Oordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add) ).

thf(498,plain,
    tc_Int_Oint @ class_OrderedGroup_Oordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(274,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(1058,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)],[274]) ).

thf(361,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).

thf(1239,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(422,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(1356,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)],[422]) ).

thf(92,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(672,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)],[92]) ).

thf(210,axiom,
    tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_p @ v_sko__local__Xmth1__2 ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mth1_0) ).

thf(919,plain,
    tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_p @ v_sko__local__Xmth1__2 ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(152,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(804,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)],[152]) ).

thf(473,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).

thf(1464,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(224,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(947,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)],[224]) ).

thf(64,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_OscaleR_0) ).

thf(604,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( D @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(166,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(831,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(251,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_1) ).

thf(1011,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) )
       != ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(419,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(1349,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)],[419]) ).

thf(49,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(567,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)],[49]) ).

thf(314,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).

thf(1144,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Oab__semigroup__mult,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(121,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(737,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)],[121]) ).

thf(22,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(509,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)],[22]) ).

thf(305,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(1122,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)],[305]) ).

thf(243,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(990,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)],[243]) ).

thf(245,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).

thf(996,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(184,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Opoly ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__minus_0) ).

thf(863,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ tc_Polynomial_Opoly @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Polynomial_Opoly ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_Polynomial_Opoly ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(330,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).

thf(1175,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(156,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(811,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)],[156]) ).

thf(477,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(1471,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)],[477]) ).

thf(130,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(758,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)],[130]) ).

thf(181,axiom,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).

thf(858,plain,
    tc_Complex_Ocomplex @ class_OrderedGroup_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(158,axiom,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__le__refl_0) ).

thf(816,plain,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( A @ ( A @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(117,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(726,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)],[117]) ).

thf(70,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(621,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)],[70]) ).

thf(175,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(848,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)],[175]) ).

thf(199,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_Oof__real ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__0_0) ).

thf(895,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_Oof__real ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(231,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Opos__bounded_0) ).

thf(964,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(416,axiom,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).

thf(1344,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Oring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(134,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(769,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)],[134]) ).

thf(331,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( C @ ( B @ c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1 ) ) @ ( 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_scaleR__right_Opos__bounded_0) ).

thf(1177,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( C @ ( B @ c_RealVector_Osko__RealVector__XscaleR__right__Xpos__bounded__1__1 ) ) @ ( 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)],[331]) ).

thf(216,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).

thf(932,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(299,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(1112,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)],[299]) ).

thf(7,axiom,
    tc_Int_Oint @ class_Int_Onumber__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Onumber__ring) ).

thf(494,plain,
    tc_Int_Oint @ class_Int_Onumber__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(284,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).

thf(1080,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(391,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Ring__and__Field_Oabs__if ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__if_0) ).

thf(1293,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Ring__and__Field_Oabs__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(90,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Ono__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors) ).

thf(668,plain,
    tc_Int_Oint @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(240,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(983,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)],[240]) ).

thf(442,axiom,
    ! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__minus__mult__self__le_0) ).

thf(1396,plain,
    ! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( A @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

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(827,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(241,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(986,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)],[241]) ).

thf(46,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(563,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)],[46]) ).

thf(480,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).

thf(1477,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(18,axiom,
    tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Ogroup__add) ).

thf(505,plain,
    tc_Int_Oint @ class_OrderedGroup_Ogroup__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(84,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(653,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)],[84]) ).

thf(86,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(658,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)],[86]) ).

thf(206,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).

thf(912,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(27,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(521,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)],[27]) ).

thf(268,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(1044,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)],[268]) ).

thf(103,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(695,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)],[103]) ).

thf(278,axiom,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) )
        = ( tc_RealDef_Oreal @ ( A @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_real__abs__def_0) ).

thf(1066,plain,
    ! [A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) )
      | ( ( tc_RealDef_Oreal @ ( A @ c_HOL_Oabs__class_Oabs ) )
        = ( tc_RealDef_Oreal @ ( A @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(464,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).

thf(1445,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(426,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).

thf(1364,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__algebra__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(366,axiom,
    tc_RealDef_Oreal @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).

thf(1250,plain,
    tc_RealDef_Oreal @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(282,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(1076,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)],[282]) ).

thf(262,axiom,
    tc_RealDef_Oreal @ ( v_r @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rp_0) ).

thf(1034,plain,
    tc_RealDef_Oreal @ ( v_r @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(397,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(1304,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)],[397]) ).

thf(214,axiom,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__norm__cancel_0) ).

thf(927,plain,
    ! [B: $i,A: $i] :
      ( ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(382,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(1277,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)],[382]) ).

thf(25,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(516,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)],[25]) ).

thf(42,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_2) ).

thf(553,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(270,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).

thf(1049,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(343,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).

thf(1203,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(345,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(1208,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)],[345]) ).

thf(58,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Orderings_Opreorder) ).

thf(589,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Orderings_Opreorder ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(34,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(531,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)],[34]) ).

thf(221,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(944,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(148,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(795,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)],[148]) ).

thf(96,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(680,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)],[96]) ).

thf(82,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oabs__if ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if) ).

thf(648,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Oabs__if ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(2,negated_conjecture,
    ! [A: $i] :
      ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ v_xa @ ( v_p @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
      = ( tc_RealDef_Oreal @ ( A @ v_x @ c_HOL_Ouminus__class_Ouminus ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(487,plain,
    ! [A: $i] :
      ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( A @ v_xa @ ( v_p @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
      = ( tc_RealDef_Oreal @ ( A @ v_x @ c_HOL_Ouminus__class_Ouminus ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(219,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).

thf(939,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(414,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(1340,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)],[414]) ).

thf(315,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(1145,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)],[315]) ).

thf(254,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).

thf(1018,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(138,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(776,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)],[138]) ).

thf(78,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(640,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)],[78]) ).

thf(257,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(1025,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Omult__mono1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__minus__right_0) ).

thf(872,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(445,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).

thf(1400,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(194,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(887,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)],[194]) ).

thf(235,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).

thf(971,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
        = B )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(368,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

thf(1252,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__algebra__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(122,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).

thf(739,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(428,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(1368,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__ring__strict ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(292,axiom,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__vector,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__vector) ).

thf(1098,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__vector,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(244,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_1) ).

thf(993,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( B @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(54,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ozero__right_0) ).

thf(580,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(180,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR_Ominus__left_0) ).

thf(855,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(108,axiom,
    tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Oab__group__add) ).

thf(705,plain,
    tc_Int_Oint @ class_OrderedGroup_Oab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(321,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).

thf(1156,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(458,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(1432,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)],[458]) ).

thf(146,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).

thf(791,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(335,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).

thf(1186,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(15,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1) ).

thf(502,plain,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(171,axiom,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).

thf(840,plain,
    ! [B: $i,A: $i] :
      ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

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

thf(1285,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(395,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(1300,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)],[395]) ).

thf(468,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(1452,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)],[468]) ).

thf(373,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(1262,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(358,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__algebra,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra) ).

thf(1235,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

thf(226,axiom,
    ! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( B @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_poly__bound__exists_0) ).

thf(951,plain,
    ! [B: $i,A: $i] : ( tc_RealDef_Oreal @ ( B @ ( A @ v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

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

thf(412,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(1336,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)],[412]) ).

thf(79,axiom,
    tc_Int_Oint @ class_Int_Oring__char__0,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Int_Oring__char__0) ).

thf(643,plain,
    tc_Int_Oint @ class_Int_Oring__char__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(39,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).

thf(544,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(204,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_RealVector_Oof__real ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).

thf(907,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_RealVector_Oof__real ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(423,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(1358,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)],[423]) ).

thf(124,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(744,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(371,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(1257,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)],[371]) ).

thf(313,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).

thf(1141,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( B @ c_lessequals ) ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(67,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(613,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)],[67]) ).

thf(352,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_1) ).

thf(1221,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(250,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(1008,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)],[250]) ).

thf(51,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(571,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)],[51]) ).

thf(379,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(1272,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)],[379]) ).

thf(10,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring) ).

thf(497,plain,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__cancel__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(182,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(859,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)],[182]) ).

thf(85,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Oring__char__0 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Int_Oring__char__0) ).

thf(656,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Oordered__idom )
      | ( A @ tc_Polynomial_Opoly @ class_Int_Oring__char__0 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(256,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(1023,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)],[256]) ).

thf(484,axiom,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).

thf(1485,plain,
    ! [A: $i] :
      ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(271,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(1052,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)],[271]) ).

thf(290,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(1094,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)],[290]) ).

thf(238,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(978,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)],[238]) ).

thf(430,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(1372,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)],[430]) ).

thf(61,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I14_J_0) ).

thf(595,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ( ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( A @ ( E @ ( D @ c_HOL_Otimes__class_Otimes ) ) @ ( C @ c_HOL_Otimes__class_Otimes ) ) @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Ocomm__semiring__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(43,axiom,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring) ).

thf(556,plain,
    ! [A: $i] :
      ( ~ ( A @ class_Ring__and__Field_Ocomm__ring )
      | ( A @ tc_Polynomial_Opoly @ class_Ring__and__Field_Ocomm__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(29,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(524,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)],[29]) ).

thf(173,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).

thf(844,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(135,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult__left_Ononneg__bounded_0) ).

thf(771,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(297,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).

thf(1108,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(237,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).

thf(976,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(202,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(903,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)],[202]) ).

thf(8,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__ring__abs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs) ).

thf(495,plain,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__ring__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(450,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(1412,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)],[450]) ).

thf(349,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add__abs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).

thf(1216,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(196,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(891,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__idom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(465,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(1448,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Ono__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(336,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( 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_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).

thf(1189,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( 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_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(381,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(1276,plain,
    tc_Complex_Ocomplex @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(408,axiom,
    ! [A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_Oof__real ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_Ozero_0) ).

thf(1326,plain,
    ! [A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_RealVector_Oof__real ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(369,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ ( C @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ( A @ ( A @ ( C @ ( B @ c_HOL_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(1253,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)],[369]) ).

thf(126,axiom,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__zero_0) ).

thf(748,plain,
    ! [A: $i] :
      ( ( ( A @ ( A @ c_HOL_Ozero__class_Ozero @ c_HOL_Ouminus__class_Ouminus ) )
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Ogroup__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(276,axiom,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( A @ c_Complex_ORe @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__Re__le__cmod_0) ).

thf(1062,plain,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( A @ c_Complex_ORe @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(482,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(1481,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__normed__div__algebra,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(363,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__of__real_0) ).

thf(1244,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( tc_RealDef_Oreal @ ( B @ c_HOL_Oabs__class_Oabs ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(141,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(781,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Oordered__comm__semiring__strict,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(230,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).

thf(961,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
       != ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_Lattices_Oboolean__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(157,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(813,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)],[157]) ).

thf(223,axiom,
    tc_RealDef_Oreal @ class_RealVector_Oreal__vector,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__vector) ).

thf(946,plain,
    tc_RealDef_Oreal @ class_RealVector_Oreal__vector,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(294,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(1101,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)],[294]) ).

thf(260,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(1030,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)],[260]) ).

thf(207,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(914,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)],[207]) ).

thf(462,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).

thf(1440,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(399,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(1308,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)],[399]) ).

thf(347,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(1212,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)],[347]) ).

thf(132,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__eq__0__iff_0) ).

thf(763,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B
        = ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero ) )
      | ( C
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(167,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(832,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)],[167]) ).

thf(98,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(684,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)],[98]) ).

thf(113,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(716,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)],[113]) ).

thf(323,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( B
        = ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).

thf(1161,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( B
        = ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ( ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) )
       != ( A @ ( C @ ( C @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oidom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(150,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(800,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)],[150]) ).

thf(301,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(1116,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)],[301]) ).

thf(309,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(1133,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)],[309]) ).

thf(246,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(999,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)],[246]) ).

thf(233,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(967,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)],[233]) ).

thf(169,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(835,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)],[169]) ).

thf(355,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).

thf(1229,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(433,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(1380,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)],[433]) ).

thf(179,axiom,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complex__mod__minus__le__complex__mod_0) ).

thf(854,plain,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ ( tc_RealDef_Oreal @ ( tc_Complex_Ocomplex @ ( A @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(317,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( D @ c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1 ) ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__right_Ononneg__bounded_1) ).

thf(1148,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( tc_RealDef_Oreal @ ( A @ ( B @ ( D @ c_RealVector_Osko__RealVector__XscaleR__right__Xnonneg__bounded__1__1 ) ) @ ( A @ ( C @ c_RealVector_Onorm__class_Onorm ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(145,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(790,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__0,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(460,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(1436,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Omult__zero,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(402,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(1314,plain,
    tc_RealDef_Oreal @ class_Ring__and__Field_Ocomm__semiring__1,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(19,axiom,
    tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add__abs,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs) ).

thf(506,plain,
    tc_Int_Oint @ class_OrderedGroup_Opordered__ab__group__add__abs,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(328,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(1172,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Olordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(325,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_Oof__real ) )
        = ( A @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real_Ominus_0) ).

thf(1165,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_Oof__real ) )
        = ( A @ ( A @ ( B @ c_RealVector_Oof__real ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(228,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(955,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)],[228]) ).

thf(388,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__interval__iff_0) ).

thf(1288,plain,
    ! [B: $i,A: $i] :
      ( ~ ( tc_RealDef_Oreal @ ( A @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ( tc_RealDef_Oreal @ ( B @ ( tc_RealDef_Oreal @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(340,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).

thf(1197,plain,
    ! [B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
      | ( A @ ( B @ ( A @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_OrderedGroup_Oordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(76,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).

thf(635,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) )
        = ( A @ ( B @ ( B @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(478,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ 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_abs__less__iff_0) ).

thf(1473,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ 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)],[478]) ).

thf(359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).

thf(1236,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A @ ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) @ ( A @ ( A @ ( C @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) @ c_lessequals ) ) )
      | ~ ( A @ class_Ring__and__Field_Olordered__ring ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(377,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(1268,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)],[377]) ).

thf(319,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_scaleR__minus__left_0) ).

thf(1152,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( A @ ( C @ ( tc_RealDef_Oreal @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_OscaleR__class_OscaleR ) ) )
        = ( A @ ( A @ ( C @ ( B @ c_RealVector_OscaleR__class_OscaleR ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
      | ~ ( A @ class_RealVector_Oreal__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(435,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).

thf(1384,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( C @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(31,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__semiring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Opordered__semiring) ).

thf(528,plain,
    tc_Int_Oint @ class_Ring__and__Field_Opordered__semiring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(80,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__ring,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Ocomm__ring) ).

thf(644,plain,
    tc_Int_Oint @ class_Ring__and__Field_Ocomm__ring,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(116,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(723,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)],[116]) ).

thf(162,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(822,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)],[162]) ).

thf(176,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(850,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)],[176]) ).

thf(248,axiom,
    ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_p @ v_sko__local__Xmth1__2 ) @ ( v_p @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
    = ( tc_RealDef_Oreal @ ( v_r @ ( v_p @ v_sko__local__Xmth1__1 ) @ c_HOL_Ouminus__class_Ouminus ) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mth1_1) ).

thf(1004,plain,
    ( ( tc_Complex_Ocomplex @ ( tc_Complex_Ocomplex @ ( v_r @ ( v_p @ v_sko__local__Xmth1__2 ) @ ( v_p @ c_Polynomial_Opoly ) ) @ c_RealVector_Onorm__class_Onorm ) )
    = ( tc_RealDef_Oreal @ ( v_r @ ( v_p @ v_sko__local__Xmth1__1 ) @ c_HOL_Ouminus__class_Ouminus ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(101,axiom,
    tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add) ).

thf(691,plain,
    tc_Int_Oint @ class_OrderedGroup_Olordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(444,axiom,
    tc_RealDef_Oreal @ class_OrderedGroup_Oordered__ab__group__add,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).

thf(1399,plain,
    tc_RealDef_Oreal @ class_OrderedGroup_Oordered__ab__group__add,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(14,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__idom,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oordered__idom) ).

thf(501,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oordered__idom,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(65,axiom,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).

thf(607,plain,
    ! [B: $i,A: $i] :
      ( ( B
        = ( A @ c_HOL_Ozero__class_Ozero ) )
      | ( ( A @ ( B @ c_HOL_Oabs__class_Oabs ) )
       != ( A @ c_HOL_Ozero__class_Ozero ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(410,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).

thf(1331,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
      | ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

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

thf(486,plain,
    ! [A: $i] : ( tc_RealDef_Oreal @ ( v_r @ ( tc_Complex_Ocomplex @ ( A @ v_xa @ c_RealVector_Onorm__class_Onorm ) @ c_lessequals ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(405,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(1320,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)],[405]) ).

thf(212,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(923,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)],[212]) ).

thf(334,axiom,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mult_Ononneg__bounded_0) ).

thf(1184,plain,
    ! [B: $i,A: $i] :
      ( ( tc_RealDef_Oreal @ ( A @ ( B @ c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 ) @ ( tc_RealDef_Oreal @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__algebra ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(265,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 @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_abs__eq__mult_2) ).

thf(1037,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 @ ( B @ c_HOL_Otimes__class_Otimes ) ) @ c_HOL_Oabs__class_Oabs ) )
        = ( A @ ( A @ ( C @ c_HOL_Oabs__class_Oabs ) @ ( A @ ( B @ c_HOL_Oabs__class_Oabs ) @ c_HOL_Otimes__class_Otimes ) ) ) )
      | ~ ( A @ class_Ring__and__Field_Opordered__ring__abs ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(466,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(1449,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)],[466]) ).

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

thf(1468,plain,
    tc_Complex_Ocomplex @ class_RealVector_Oreal__normed__vector,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(110,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_RealVector_Oof__real ) )
       != ( A @ ( C @ c_RealVector_Oof__real ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__real__eq__iff_0) ).

thf(708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( B = C )
      | ( ( A @ ( B @ c_RealVector_Oof__real ) )
       != ( A @ ( C @ c_RealVector_Oof__real ) ) )
      | ~ ( A @ class_RealVector_Oreal__algebra__1 ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(192,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(882,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)],[192]) ).

thf(4,axiom,
    tc_Int_Oint @ class_Orderings_Olinorder,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Orderings_Olinorder) ).

thf(491,plain,
    tc_Int_Oint @ class_Orderings_Olinorder,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(288,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(1088,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)],[288]) ).

thf(9,axiom,
    tc_Int_Oint @ class_Ring__and__Field_Oring__no__zero__divisors,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors) ).

thf(496,plain,
    tc_Int_Oint @ class_Ring__and__Field_Oring__no__zero__divisors,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(279,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(1069,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)],[279]) ).

thf(252,axiom,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).

thf(1014,plain,
    ! [B: $i,A: $i] :
      ( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_RealVector_Onorm__class_Onorm ) )
        = ( A @ ( B @ c_RealVector_Onorm__class_Onorm ) ) )
      | ~ ( A @ class_RealVector_Oreal__normed__vector ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(452,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(1417,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)],[452]) ).

thf(1901,plain,
    $false,
    inference(e,[status(thm)],[1322,1036,809,1469,1454,846,628,893,1083,1179,1110,645,892,1168,760,1315,518,523,1406,1290,1443,1422,1073,1205,677,1437,861,1173,878,511,1310,550,500,1233,698,1342,945,1063,930,1458,1164,797,538,1354,829,898,1001,1391,782,1386,1475,565,1265,1482,885,1046,1409,570,1430,1298,719,785,504,802,1279,949,917,702,751,934,1191,817,1087,1147,1247,870,1479,1362,638,853,969,1347,1415,492,591,1040,623,514,574,806,966,1283,905,1302,756,1136,834,766,687,1377,692,734,866,1394,1351,660,1405,1201,507,527,1119,774,1345,988,920,942,678,529,793,925,1306,1199,1338,534,714,1057,1274,1223,1091,825,1255,820,561,1487,630,1370,729,1238,1387,910,1021,778,1042,952,1217,598,916,566,1032,1365,625,879,852,583,889,1159,1079,1128,1281,1291,842,974,1106,1296,665,493,1210,682,1195,1402,1360,742,697,650,1017,615,1121,980,1425,1096,1006,593,869,610,1118,499,1397,1270,1259,1329,1028,488,753,1182,669,901,1214,706,1419,1461,537,1155,547,837,1263,1099,701,1297,1451,1131,1192,1060,721,779,1324,1114,1150,1249,1456,1382,1266,1231,503,1393,1333,1434,1318,1086,1241,633,508,541,1054,1170,674,1026,530,662,1286,1035,1466,558,1071,773,586,1135,1103,1219,745,689,1374,601,1251,618,584,819,732,1125,1388,958,1226,875,577,711,1428,1139,936,1312,787,498,1058,1239,1356,672,919,804,1464,947,604,831,1011,1349,567,1144,737,509,1122,990,996,863,1175,811,1471,758,858,816,726,621,848,895,964,1344,769,1177,932,1112,494,1080,1293,668,983,1396,827,986,563,1477,505,653,658,912,521,1044,695,1066,1445,1364,1250,1076,1034,1304,927,1277,516,553,1049,1203,1208,589,531,944,795,680,648,487,939,1340,1145,1018,776,640,1025,872,1400,887,971,1252,739,1368,1098,993,580,855,705,1156,1432,791,1186,502,840,1285,1300,1452,1262,1235,951,808,1336,643,544,907,1358,744,1257,1141,613,1221,1008,571,1272,497,859,656,1023,1485,1052,1094,978,1372,595,556,524,844,771,1108,976,903,495,1412,1216,891,1448,1189,1276,1326,1253,748,1062,1481,1244,781,961,813,946,1101,1030,914,1440,1308,1212,763,832,684,716,1161,800,1116,1133,999,967,835,1229,1380,854,1148,790,1436,1314,506,1172,1165,955,1288,1197,635,1473,1236,1268,1152,1384,528,644,723,822,850,1004,691,1399,501,607,1331,486,1320,923,1184,1037,1449,1468,708,882,491,1088,496,1069,1014,1417]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04  % Problem  : ALG373-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.12  % Command  : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p  --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.23/0.49  % Computer : n009.cluster.edu
% 0.23/0.49  % Model    : x86_64 x86_64
% 0.23/0.49  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.49  % Memory   : 8046.5625MB
% 0.23/0.49  % OS       : Linux 6.8.0-71-generic
% 0.23/0.49  % CPULimit : 300
% 0.23/0.49  % WCLimit  : 300
% 0.23/0.49  % DateTime : Sat Sep 26 21:56:00 UTC 2026
% 0.23/0.49  % CPUTime  : 
% 0.23/0.49  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
% 1.37/1.32  % [INFO] 	 Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ... 
% 2.81/1.84  % [INFO] 	 Parsing done (513ms). 
% 2.81/1.86  % [INFO] 	 Running in sequential loop mode. 
% 4.26/2.42  % [INFO] 	 eprover registered as external prover. 
% 4.26/2.43  % [INFO] 	 Scanning for conjecture ... 
% 4.65/2.66  % [INFO] 	 Found a conjecture (or negated_conjecture) and 482 axioms. Running axiom selection ... 
% 5.66/2.92  % [INFO] 	 Axiom selection finished. Selected 482 axioms (removed 0 axioms). 
% 7.01/3.23  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 7.01/3.25  % [INFO] 	 Type checking passed. 
% 7.01/3.26  % [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 ... 
% 31.96/8.47  % External prover 'e' found a proof!
% 31.96/8.47  % [INFO] 	 Killing All external provers ... 
% 31.96/8.47  % Time passed: 7779ms (effective reasoning time: 6606ms)
% 31.96/8.48  % Axioms used in derivation (482): cls_abs__le__zero__iff_0, cls_mult__less__cancel__left__disj_5, clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add, cls_xt1_I9_J_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oidom, cls_linorder__antisym__conv2_1, cls_minus__le__iff_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring__strict, clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if, cls_neg__0__le__iff__le_1, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__semiring, cls_mult__zero__right_0, cls_mult__left_Ononneg__bounded_1, cls_order__le__less__trans_0, clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add__abs, cls_abs__if__lattice_0, cls_abs__le__iff_2, clsarity_Int__Oint__Int_Onumber, cls_order__less__le__trans_0, cls_order__eq__iff_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_le__minus__self__iff_0, cls_abs__Re__le__cmod_0, clsarity_RealDef__Oreal__Orderings_Opreorder, cls_mult__nonneg__nonneg_0, cls_mult__right__mono_0, cls_mult__right_Ozero_0, cls_scaleR__cancel__left_0, cls_mult__left_Obounded_0, cls_abs__of__nonneg_0, cls_real__mult__le__cancel__iff1_0, cls_xt1_I12_J_0, cls_mult__less__cancel__right__disj_0, cls_mult__nonneg__nonpos2_0, cls_scaleR__cancel__right_1, cls_real__less__def_1, cls_zero__less__norm__iff_1, clsarity_Int__Oint__Ring__and__Field_Oabs__if, clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1, cls_square__eq__iff_1, cls_real__mult__le__cancel__iff2_1, cls_minus__zero_0, cls_norm__zero_0, cls_scaleR__right_Obounded_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oring, clsarity_Polynomial__Opoly__Orderings_Olinorder, clsarity_Int__Oint__Ring__and__Field_Olordered__ring, cls_real__mult__assoc_0, clsarity_Complex__Ocomplex__Int_Onumber, cls_class__semiring_Osemiring__rules_I9_J_0, cls_mult__less__cancel__left__disj_1, clsarity_RealDef__Oreal__RealVector_Oreal__vector, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring__1, cls_zero__le__mult__iff_3, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring, cls_CHAINED_0, clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add, clsarity_Int__Oint__Ring__and__Field_Opordered__ring, cls_abs__minus__le__zero_0, cls_linorder__neqE_0, clsarity_Int__Oint__Orderings_Oorder, clsarity_Polynomial__Opoly__OrderedGroup_Ogroup__add, cls_abs__eq__mult_1, cls_real__le__trans_0, clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add, cls_abs__mult__less_0, cls_compl__eq__compl__iff_0, cls_mult__nonpos__nonneg_0, cls_mult__scaleR__right_0, cls_minus__le__self__iff_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_of__real__0_0, cls_real__mult__less__iff1_0, clsarity_Polynomial__Opoly__OrderedGroup_Oab__group__add, cls_mult__nonpos__nonpos_0, cls_minus__minus_0, clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, cls_mult__right_OscaleR_0, cls_order__less__trans_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_abs__of__pos_0, cls_neg__less__iff__less_1, cls_scaleR_Ominus__left_0, cls_real__mult__le__cancel__iff2_0, clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs, clsarity_Complex__Ocomplex__RealVector_Oreal__vector, cls_mult__less__imp__less__right_0, cls_real__vector_Oscale__scale_0, cls_less__minus__iff_0, cls_mult_Ononneg__bounded_0, cls_mult__le__cancel__left__pos_0, cls_scaleR__eq__0__iff_0, cls_split__mult__neg__le_0, cls_mult__less__cancel__left__disj_4, cls_abs__le__interval__iff_0, clsarity_Int__Oint__Ring__and__Field_Ocomm__ring, cls_mult__less__cancel__right__disj_3, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult, cls_mult__eq__0__iff_0, clsarity_Int__Oint__Ring__and__Field_Oring__no__zero__divisors, cls_abs__less__iff_2, cls_mult__left_Opos__bounded_0, cls_mult__less__imp__less__left_0, cls_real__minus__mult__self__le_0, cls_mult__mono_0, clsarity_Int__Oint__OrderedGroup_Olordered__ab__group__add__abs, clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__1, cls_neg__equal__iff__equal_0, clsarity_Int__Oint__Ring__and__Field_Oordered__semiring__strict, cls_linorder__not__less_0, cls_of__real__minus_0, cls_class__semiring_Omul__0_0, cls_poly__bound__exists_1, cls_order__less__asym_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_mult__left__mono__neg_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring, cls_scaleR_Ominus__right_0, cls_mult_Ozero__left_0, cls_zero__le__mult__iff_0, cls_order__less__asym_H_0, cls_mult__left__mono_0, cls_mult_OscaleR__right_0, cls_real__le__linear_0, cls_mult__strict__right__mono_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors, cls_scaleR__cancel__right_0, cls_class__semiring_Omul__c_0, cls_linorder__antisym__conv2_0, cls_scaleR__right_Opos__bounded_1, cls_mult__pos__neg_0, cls_order__eq__refl_0, cls_mult__strict__mono_0, clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero, clsarity_Int__Oint__Ring__and__Field_Omult__mono, cls_order__le__less_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra, cls_eq__number__of_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1, cls_mult_Ozero__right_0, cls_linorder__antisym__conv1_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__idom, cls_minus__less__iff_1, cls_abs__eq__mult_0, cls_real__less__def_0, cls_neg__0__le__iff__le_0, cls_of__real__eq__0__iff_0, cls_less__le__not__le_2, cls_xt1_I10_J_0, cls_mult__right_Obounded_0, cls_norm__ge__zero_0, clsarity_RealDef__Oreal__Int_Onumber, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict, cls_zero__le__mult__iff_4, cls_neg__less__eq__nonneg_1, clsarity_Int__Oint__Int_Oring__char__0, cls_le__minus__iff_0, cls_neg__less__eq__nonneg_0, cls_mult__left_Ononneg__bounded_0, cls_not__less__iff__gr__or__eq_0, cls_complex__mod__minus__le__complex__mod_0, cls_scaleR__minus__right_0, cls_no__zero__divisors_0, clsarity_Polynomial__Opoly__OrderedGroup_Oab__semigroup__mult, clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_abs__le__interval__iff_2, cls_real__abs__def_0, cls_mult__le__0__iff_0, cls_real__le__refl_0, cls_mult__neg__pos_0, cls_norm__not__less__zero_0, clsarity_Int__Oint__OrderedGroup_Oab__semigroup__mult, cls_mult__right__le__imp__le_0, cls_abs__norm__cancel_0, cls_abs__eq__0_0, cls_of__real_Ozero_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring, cls_minus__mult__commute_0, cls_le__minus__iff_1, clsarity_Int__Oint__Ring__and__Field_Ono__zero__divisors, clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1, cls_abs__ge__minus__self_0, cls_neg__le__0__iff__le_0, cls_real__mult__less__mono2_0, 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_Osemiring__rules_I19_J_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, cls_mult__le__cancel__left__neg_1, clsarity_Complex__Ocomplex__Int_Oring__char__0, clsarity_Polynomial__Opoly__OrderedGroup_Oordered__ab__group__add, cls_class__semiring_Osemiring__rules_I17_J_0, clsarity_Int__Oint__Ring__and__Field_Opordered__semiring, cls_calculation_0, cls_zero__less__abs__iff_0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_mult__left__idem_0, cls_xt1_I8_J_0, cls_mult__left_Opos__bounded_1, 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, cls_split__mult__pos__le_0, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring__abs, cls_mult__left_OscaleR_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs, clsarity_Polynomial__Opoly__Ring__and__Field_Ono__zero__divisors, clsarity_RealDef__Oreal__Int_Oring__char__0, cls_neg__0__less__iff__less_0, cls_neg__less__0__iff__less_0, cls_neg__equal__0__iff__equal_0, cls_abs__idempotent_0, cls_mult__le__0__iff_4, cls_linorder__linear_0, clsarity_Polynomial__Opoly__Int_Onumber, clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1, cls_real__mult__less__iff1_1, cls_mult_Ominus__right_0, clsarity_Int__Oint__OrderedGroup_Ogroup__add, cls_le__minus__self__iff_1, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1, cls_not__leE_0, cls_mult__less__cancel__right__disj_2, cls_minus__le__self__iff_1, cls_order__antisym_0, cls_order__trans_0, clsarity_Int__Oint__Ring__and__Field_Omult__zero, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, cls_mult__left__less__imp__less_0, cls_mult__strict__left__mono_0, cls_of__real__mult_0, cls_le__number__of__eq__not__less_1, cls_neg__equal__zero_1, cls_real__mult__order_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oabs__if, cls_mult_Ononneg__bounded_1, cls_abs__minus__cancel_0, cls_linorder__antisym__conv1_1, cls_split__mult__pos__le_1, cls_no__zero__divirors__neq0_0, cls_mult__le__0__iff_5, clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector, cls_mult__strict__mono_H_0, cls_abs__if_1, cls_real__mult__left__cancel_0, cls_abs__ge__zero_0, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__ring__strict, cls_mult__right_Ominus_0, cls_abs__eq__mult_3, cls_real__mult__right__cancel_0, cls_linorder__not__le_1, clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add, cls_scaleR__right_Opos__bounded_0, clsarity_Int__Oint__Orderings_Olinorder, cls_minus__less__iff_0, cls_mult__less__cancel__right__disj_5, cls_scaleR__left_Ominus_0, cls_abs__ge__self_0, cls_class__semiring_Omul__a_0, cls_not__less__iff__gr__or__eq_1, cls_neg__0__equal__iff__equal_1, cls_zero__le__square_0, cls_less__eq__neg__nonpos_1, cls_equation__minus__iff_0, cls_mth1_0, cls_less__minus__iff_1, cls_scaleR_Ozero__right_0, clsarity_Int__Oint__Ring__and__Field_Oordered__ring__strict, cls_scaleR__conv__of__real_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oidom, cls_scaleR__eq__0__iff_2, cls_order__le__neq__trans_0, cls_scaleR__right_Ononneg__bounded_0, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__ring, cls_mult__nonneg__nonpos_0, cls_real__abs__def_1, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__zero, cls_abs__of__nonpos_0, cls_real__sum__squares__cancel__a_1, cls_order__eq__iff_2, clsarity_RealDef__Oreal__Ring__and__Field_Oidom, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono, cls_linorder__neqE__ordered__idom_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__ring__1, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__ring__1, clsarity_Int__Oint__Ring__and__Field_Ocomm__semiring__0, cls_less__le__not__le_1, cls_abs__less__iff_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring, cls_mult__eq__0__iff_2, cls_not__square__less__zero_0, cls_linorder__antisym__conv3_0, clsarity_Int__Oint__Orderings_Opreorder, cls_order__neq__le__trans_0, cls_mult_Opos__bounded_1, cls_mult__mono_H_0, cls_neg__le__0__iff__le_1, cls_mult__right_Ononneg__bounded_0, cls_order__antisym__conv_0, cls_abs__le__D2_0, cls_of__real_Ominus_0, clsarity_Int__Oint__Ring__and__Field_Opordered__ring__abs, cls_mult__strict__left__mono__comm_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_abs__mult__self_0, cls_mult__less__cancel__left__neg_1, cls_abs__not__less__zero_0, cls_abs__number__of_1, cls_abs__le__mult_0, cls_complex__Re__le__cmod_0, cls_le__imp__neg__le_0, cls_not__real__square__gt__zero_1, cls_linorder__less__linear_0, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__ring, cls_mult_Ominus__left_0, cls_abs__mult__pos_0, clsarity_Int__Oint__Ring__and__Field_Opordered__cancel__semiring, cls_poly__minus_0, cls_order__less__le_2, cls_zero__le__mult__iff_5, clsarity_Polynomial__Opoly__Int_Oring__char__0, cls_mult__less__cancel__left__pos_1, clsarity_Int__Oint__Int_Onumber__ring, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__0, cls_norm__mult_0, cls_neg__0__less__iff__less_1, cls_zero__le__mult__iff_1, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector, cls_abs__if__lattice_1, cls_minus__mult__left_0, cls_xt1_I11_J_0, clsarity_Int__Oint__Ring__and__Field_Oring, cls_norm__eq__zero_0, cls_mult__le__cancel__left__neg_0, cls_zero__less__abs__iff_1, cls_mult__le__0__iff_2, cls_mult__scaleR__left_0, cls_class__semiring_Osemiring__rules_I18_J_0, cls_mult__right_Opos__bounded_1, cls_neg__less__0__iff__less_1, clsarity_Int__Oint__Ring__and__Field_Oordered__comm__semiring__strict, cls_real__le__antisym_0, cls_xt1_I6_J_0, cls_minus__mult__right_0, cls_double__compl_0, clsarity_Int__Oint__OrderedGroup_Oordered__ab__group__add, cls_zero__less__mult__pos2_0, cls_mult__left_Ominus_0, cls_mult__right__mono__neg_0, cls_abs__mult_0, cls_neg__equal__zero_0, cls_mult__less__cancel__left__disj_3, cls_norm__mult__ineq_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__0, cls_mult__less__cancel__right__disj_4, cls_scaleR__cancel__left_1, cls_rabs__ratiotest__lemma_0, cls_abs__if_0, clsarity_Polynomial__Opoly__Orderings_Oorder, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add, cls_real__sum__squares__cancel__a_0, cls_mult__zero__left_0, cls_of__real__eq__iff_0, cls_norm__le__zero__iff_1, cls_linorder__not__le_0, cls_scaleR_Ozero__left_0, cls_minus__le__iff_1, clsarity_Polynomial__Opoly__Int_Onumber__ring, cls_abs__number__of_0, cls_less__eq__neg__nonpos_0, cls_norm__mult__less_0, clsarity_Int__Oint__Ring__and__Field_Oidom, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult, clsarity_Int__Oint__Ring__and__Field_Ocomm__ring__1, cls_norm__scaleR_0, clsarity_Int__Oint__OrderedGroup_Oab__group__add, cls_mult__pos__pos_0, cls_neg__0__equal__iff__equal_0, cls_mult__left__le__imp__le_0, cls_neg__le__iff__le_0, clsarity_Polynomial__Opoly__Orderings_Opreorder, cls_less__minus__self__iff_1, cls_order__less__irrefl_0, cls_norm__of__real_0, clsarity_Int__Oint__Ring__and__Field_Omult__mono1, cls_mult__strict__right__mono__neg_0, cls_mult__right_Ononneg__bounded_1, cls_norm__ratiotest__lemma_0, cls_mult__right__less__imp__less_0, cls_equation__minus__iff_1, clsarity_Polynomial__Opoly__Ring__and__Field_Ocomm__semiring__0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom, cls_less__minus__self__iff_0, clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add, cls_mult__less__cancel__left__disj_2, cls_real__mult__commute_0, cls_real__mult__le__cancel__iff1_1, cls_abs__le__zero__iff_1, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add__abs, cls_scaleR_OscaleR__right_0, clsarity_Polynomial__Opoly__Ring__and__Field_Opordered__cancel__semiring, cls_abs__eq__0_1, cls_mult__less__cancel__right__disj_1, cls_abs__leI_0, clsarity_RealDef__Oreal__Orderings_Oorder, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring, cls_mult__eq__0__iff_1, cls_scaleR__minus__left_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring, cls_real__less__def_2, clsarity_Polynomial__Opoly__OrderedGroup_Opordered__ab__group__add, clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add, cls_norm__le__zero__iff_0, cls_order__less__imp__le_0, cls_abs__le__D1_0, cls_minus__equation__iff_1, cls_abs__eq__mult_2, cls_not__real__square__gt__zero_0, cls_mult_Obounded_0, cls_mult__idem_0, clsarity_RealDef__Oreal__Int_Onumber__ring, cls_minus__mult__minus_0, clsarity_Int__Oint__OrderedGroup_Opordered__ab__group__add, cls_zero__less__norm__iff_0, cls_norm__minus__cancel_0, cls_scaleR__eq__0__iff_1, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__semiring, cls_rp_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors, clsarity_Polynomial__Opoly__Ring__and__Field_Oordered__comm__semiring__strict, cls_square__eq__iff_0, cls_xt1_I7_J_0, cls_mult_OscaleR__left_0, cls_scaleR__left__commute_0, cls_mult__less__le__imp__less_0, clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, clsarity_Int__Oint__Ring__and__Field_Oordered__semiring, cls_mult_Opos__bounded_0, clsarity_Polynomial__Opoly__Ring__and__Field_Omult__mono1, cls_mult__right_Opos__bounded_0, cls_scaleR__right_OscaleR_0, clsarity_Complex__Ocomplex__RealVector_Oreal__algebra, cls_mth1_1, 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_neg__less__iff__less_0, clsarity_Int__Oint__Ring__and__Field_Oordered__idom, cls_scaleR__right_Ononneg__bounded_1, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs, cls_split__mult__neg__le_1, clsarity_Polynomial__Opoly__Ring__and__Field_Oring__no__zero__divisors, cls_poly__bound__exists_0, cls_zero__le__mult__iff_2, 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, cls_abs__of__neg_0, cls_abs__less__iff_1, cls_mult__less__cancel__left__pos_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict, cls_le__number__of__eq__not__less_0, cls_abs__le__interval__iff_1, clsarity_RealDef__Oreal__RealVector_Oreal__algebra
% 31.96/8.48  % No. of inferences in proof: 971
% 31.96/8.48  % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7779 ms resp. 6606 ms w/o parsing
% 32.14/8.84  % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.14/8.85  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------