TSTP Solution File: ALG371-1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ALG371-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n017.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Mon May 20 18:15:03 EDT 2024

% Result   : Unsatisfiable 12.72s 4.32s
% Output   : Refutation 14.12s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  572
% Syntax   : Number of formulae    : 1077 ( 171 unt;  68 typ;   0 def)
%            Number of atoms       : 3231 ( 408 equ;   0 cnn)
%            Maximal formula atoms :    6 (   3 avg)
%            Number of connectives : 16132 (2018   ~;2222   |;   0   &;11892   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   17 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   81 (  81   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   70 (  68 usr;   6 con; 0-3 aty)
%            Number of variables   : 2754 (   0   ^2754   !;   0   ?;2754   :)

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

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

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

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

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

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

thf(v_x_type,type,
    v_x: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1_type,type,
    c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1: $i > $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1_type,type,
    v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1: $i > $i > $i ).

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

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

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

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

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

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

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

thf(44,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I13_J_0) ).

thf(629,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(446,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).

thf(1469,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(439,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).

thf(1454,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(268,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).

thf(1105,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(230,axiom,
    class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).

thf(1031,plain,
    class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).

thf(163,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).

thf(893,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).

thf(302,axiom,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1) ).

thf(1179,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(360,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos_0) ).

thf(1295,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(486,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__pos_0) ).

thf(1549,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(398,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).

thf(1369,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(308,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ( c_lessequals @ B @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__linear_0) ).

thf(1190,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ( c_lessequals @ B @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(370,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).

thf(1315,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_1) ).

thf(518,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(257,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_4) ).

thf(1083,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(197,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A )
        = B )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).

thf(962,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A )
        = B )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(489,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).

thf(1554,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(270,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).

thf(1110,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(314,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_2) ).

thf(1200,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(205,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).

thf(977,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).

thf(85,axiom,
    class_Ring__and__Field_Oidom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).

thf(730,plain,
    class_Ring__and__Field_Oidom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(249,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).

thf(1068,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(472,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).

thf(1522,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(423,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_1) ).

thf(1422,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).

thf(483,axiom,
    class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors) ).

thf(1544,plain,
    class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(317,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).

thf(1205,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(477,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).

thf(1533,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).

thf(431,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__zero__iff_0) ).

thf(1437,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(235,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_0) ).

thf(1041,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(292,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__right__mono_0) ).

thf(1158,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(100,axiom,
    class_Ring__and__Field_Osgn__if @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if) ).

thf(762,plain,
    class_Ring__and__Field_Osgn__if @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(39,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__a_0) ).

thf(614,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(60,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__cancel_0) ).

thf(677,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).

thf(460,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing2_0) ).

thf(1497,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).

thf(254,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).

thf(1078,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I1_J_0) ).

thf(533,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(330,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
        = B )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).

thf(1233,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
        = B )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).

thf(376,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_1) ).

thf(1327,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).

thf(342,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__less__imp__less_0) ).

thf(1260,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(190,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_1) ).

thf(945,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).

thf(247,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__0_0) ).

thf(1063,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).

thf(390,axiom,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal__of__preal @ A ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__preal__zero__less_0) ).

thf(1354,plain,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal__of__preal @ A ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(296,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).

thf(1164,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(119,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).

thf(797,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(383,axiom,
    class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

thf(1342,plain,
    class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(94,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_0) ).

thf(747,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).

thf(311,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).

thf(1196,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(167,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transcendental_Oln @ A ) @ ( c_Transcendental_Oln @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ln__le__cancel__iff_1) ).

thf(898,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transcendental_Oln @ A ) @ ( c_Transcendental_Oln @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(500,axiom,
    class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra) ).

thf(1576,plain,
    class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(433,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).

thf(1441,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).

thf(139,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_1) ).

thf(841,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(393,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_2) ).

thf(1359,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(475,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono1_0) ).

thf(1529,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono1 @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(334,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).

thf(1243,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(278,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__pos_0) ).

thf(1127,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(203,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_2) ).

thf(973,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(159,axiom,
    class_Ring__and__Field_Oordered__idom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom) ).

thf(885,plain,
    class_Ring__and__Field_Oordered__idom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).

thf(238,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).

thf(1046,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).

thf(328,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).

thf(1228,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).

thf(453,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osgn__if @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn0_0) ).

thf(1482,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Osgn__if @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(355,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing2_0) ).

thf(1287,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(427,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).

thf(1430,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(113,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).

thf(785,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(344,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).

thf(1264,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).

thf(121,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).

thf(802,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(369,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).

thf(1313,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(501,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).

thf(1577,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(184,axiom,
    class_Ring__and__Field_Ono__zero__divisors @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors) ).

thf(934,plain,
    class_Ring__and__Field_Ono__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(15,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__divide_0) ).

thf(542,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(417,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__power__not__zero_0) ).

thf(1409,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1__no__zero__divisors @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(81,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).

thf(724,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(30,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Osgn__class_Osgn @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__mult_0) ).

thf(587,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Osgn__class_Osgn @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).

thf(374,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__divide_0) ).

thf(1323,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(467,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal )
       != ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__left__cancel_0) ).

thf(1511,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal )
       != ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(176,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).

thf(917,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).

thf(442,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(1462,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(245,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__neg_0) ).

thf(1059,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).

thf(280,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).

thf(1132,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(484,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__pos_0) ).

thf(1545,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(128,axiom,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__refl_0) ).

thf(817,plain,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(47,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__commute_0) ).

thf(638,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).

thf(287,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ E @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less_0) ).

thf(1147,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ E @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(372,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).

thf(1319,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(157,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).

thf(881,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(273,axiom,
    class_Orderings_Opreorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).

thf(1115,plain,
    class_Orderings_Opreorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(259,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_RealDef_Oreal__of__preal @ B ) @ tc_RealDef_Oreal )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__all__real2_0) ).

thf(1087,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_RealDef_Oreal__of__preal @ B ) @ tc_RealDef_Oreal )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).

thf(468,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono_0) ).

thf(1514,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(200,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors) ).

thf(969,plain,
    class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(498,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).

thf(1572,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(456,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__power_0) ).

thf(1489,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(444,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ C @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ C @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__trans_0) ).

thf(1465,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ C @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ C @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(115,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_0) ).

thf(789,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(437,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).

thf(1450,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).

thf(400,axiom,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1) ).

thf(1373,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).

thf(1334,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(289,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
       != ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
      | ( D = E )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__scale__eq__noteq_0) ).

thf(1151,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
       != ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
      | ( D = E )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(405,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).

thf(1383,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(123,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).

thf(806,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(503,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).

thf(1581,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(130,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors) ).

thf(821,plain,
    class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(170,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_3) ).

thf(905,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(364,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pos__add__strict_0) ).

thf(1302,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(98,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__imp__less__base_0) ).

thf(756,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).

thf(421,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).

thf(1418,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(42,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mult__distrib_0) ).

thf(623,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(282,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).

thf(1136,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

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

thf(834,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_1) ).

thf(1183,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ C @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_1) ).

thf(1283,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ C @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(64,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Oln @ A ) @ ( c_Transcendental_Oln @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ln__less__cancel__iff_1) ).

thf(687,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Oln @ A ) @ ( c_Transcendental_Oln @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(322,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__iff_1) ).

thf(1215,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).

thf(155,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).

thf(877,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(194,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_0) ).

thf(956,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).

thf(866,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(251,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).

thf(1072,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(275,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).

thf(1119,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(410,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).

thf(1394,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(143,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__less__imp__less_0) ).

thf(849,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(3,negated_conjecture,
    ~ ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ ( c_Polynomial_Opoly @ v_p @ ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ ( c_RealVector_Onorm__class_Onorm @ ( c_Polynomial_Opoly @ v_p @ v_x @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).

thf(507,plain,
    ~ ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ ( c_Polynomial_Opoly @ v_p @ ( c_HOL_Ozero__class_Ozero @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ ( c_RealVector_Onorm__class_Onorm @ ( c_Polynomial_Opoly @ v_p @ v_x @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__a_0) ).

thf(527,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(35,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
       != ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
      | ( C = E )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_0) ).

thf(602,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
       != ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
      | ( C = E )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).

thf(207,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ tc_RealDef_Oreal )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__norm__iff_1) ).

thf(981,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ tc_RealDef_Oreal )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).

thf(103,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).

thf(766,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(252,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).

thf(1074,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(117,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_0) ).

thf(793,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(180,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).

thf(925,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(366,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).

thf(1306,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(313,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).

thf(1199,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).

thf(125,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).

thf(810,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).

thf(368,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).

thf(1311,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(5,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I17_J_0) ).

thf(512,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(189,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).

thf(942,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(244,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).

thf(1057,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(295,axiom,
    class_Ring__and__Field_Omult__mono @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono) ).

thf(1163,plain,
    class_Ring__and__Field_Omult__mono @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).

thf(349,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).

thf(1274,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).

thf(407,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__ge__zero_0) ).

thf(1387,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(471,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_RealVector_Onorm__class_Onorm @ D @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__ratiotest__lemma_0) ).

thf(1519,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_RealVector_Onorm__class_Onorm @ D @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(340,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I5_J_0) ).

thf(1255,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(148,axiom,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__zero_0) ).

thf(862,plain,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).

thf(323,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Oln @ A ) @ ( c_Transcendental_Oln @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ln__less__cancel__iff_0) ).

thf(1217,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Oln @ A ) @ ( c_Transcendental_Oln @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(463,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).

thf(1502,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).

thf(455,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_0) ).

thf(1487,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(67,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__pos__nonneg_0) ).

thf(693,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).

thf(127,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__double__add__iff__zero__less__single__add_1) ).

thf(815,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(84,axiom,
    class_OrderedGroup_Oab__group__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).

thf(729,plain,
    class_OrderedGroup_Oab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(492,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_1) ).

thf(1560,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(326,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__neg__neg_0) ).

thf(1223,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).

thf(164,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__less__imp__less_0) ).

thf(894,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(132,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I6_J_0) ).

thf(825,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(384,axiom,
    class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra) ).

thf(1343,plain,
    class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(224,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).

thf(1021,plain,
    class_OrderedGroup_Omonoid__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(110,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).

thf(778,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(391,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos2_0) ).

thf(1355,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(502,axiom,
    class_Ring__and__Field_Ozero__neq__one @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one) ).

thf(1580,plain,
    class_Ring__and__Field_Ozero__neq__one @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(497,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__square_0) ).

thf(1570,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(300,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).

thf(1174,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(175,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

thf(916,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(231,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).

thf(1032,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(396,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__neg_0) ).

thf(1365,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(156,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_1) ).

thf(879,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(490,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonneg_0) ).

thf(1555,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(56,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__imp__eq_0) ).

thf(665,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__ab__semigroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(440,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__less_1) ).

thf(1457,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(134,axiom,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__sgn_0) ).

thf(830,plain,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).

thf(889,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(319,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__less__mono_0) ).

thf(1210,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(18,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__left_0) ).

thf(551,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(409,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).

thf(1392,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(142,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal )
      = ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__commute_0) ).

thf(847,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal )
      = ( c_HOL_Otimes__class_Otimes @ B @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(23,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__mult__class_Omult__ac_I1_J_0) ).

thf(566,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__mult @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(62,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__left__mono__comm_0) ).

thf(682,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__comm__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(416,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonpos2_0) ).

thf(1407,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(357,axiom,
    class_Orderings_Olinorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).

thf(1291,plain,
    class_Orderings_Olinorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(75,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).

thf(710,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(414,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_0) ).

thf(1402,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).

thf(388,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__neg_0) ).

thf(1350,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(260,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add) ).

thf(1089,plain,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(347,axiom,
    class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

thf(1270,plain,
    class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(425,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
      | ( ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__mult_0) ).

thf(1425,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__div__algebra @ A )
      | ( ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(264,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).

thf(1096,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(217,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).

thf(1006,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_1) ).

thf(1138,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(32,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__d_0) ).

thf(593,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(112,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).

thf(783,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(412,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).

thf(1397,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

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

thf(742,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(27,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__num_0) ).

thf(578,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(154,axiom,
    ! [A: $i] :
      ( ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_0) ).

thf(874,plain,
    ! [A: $i] :
      ( ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(285,axiom,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_1) ).

thf(1143,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).

thf(51,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_1) ).

thf(650,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).

thf(948,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(496,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_2) ).

thf(1567,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(458,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).

thf(1493,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(377,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
       != ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ E @ A )
        = ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).

thf(1329,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
       != ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ E @ A )
        = ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(293,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_4) ).

thf(1160,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(228,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_H_0) ).

thf(1028,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(394,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_0) ).

thf(1361,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(358,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring) ).

thf(1292,plain,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).

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

thf(554,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(304,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).

thf(1182,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(424,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(1424,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(419,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).

thf(1414,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(321,axiom,
    class_OrderedGroup_Olordered__ab__group__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add) ).

thf(1214,plain,
    class_OrderedGroup_Olordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(201,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg_0) ).

thf(970,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(73,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).

thf(706,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(222,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_0) ).

thf(1016,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

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

thf(590,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(265,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__less__zero__iff__single__less__zero_0) ).

thf(1099,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(71,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).

thf(701,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(361,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono__neg_0) ).

thf(1297,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).

thf(89,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ B @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).

thf(738,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ B @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(481,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__right_0) ).

thf(1539,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(309,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_0) ).

thf(1192,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).

thf(240,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).

thf(1050,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(24,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I25_J_0) ).

thf(569,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).

thf(1246,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(36,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oadd__right_0) ).

thf(605,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).

thf(50,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__commutes_0) ).

thf(647,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ B @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).

thf(214,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__left_0) ).

thf(997,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(6,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
        = ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__c_0) ).

thf(515,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
        = ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(451,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).

thf(1478,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(208,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_5) ).

thf(984,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(173,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( B
       != ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_0) ).

thf(911,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( B
       != ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(429,axiom,
    class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

thf(1434,plain,
    class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(315,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__increasing_0) ).

thf(1202,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).

thf(187,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ E @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less2_0) ).

thf(938,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ E @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).

thf(333,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__mono_0) ).

thf(1241,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).

thf(178,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_1) ).

thf(921,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(494,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).

thf(1563,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(298,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_1) ).

thf(1170,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_0) ).

thf(1035,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(11,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).

thf(530,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(107,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono_0) ).

thf(773,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(102,axiom,
    class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one) ).

thf(765,plain,
    class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(242,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__mono_0) ).

thf(1054,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(307,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_1) ).

thf(1187,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(59,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I8_J_0) ).

thf(674,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(227,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__le__imp__less_0) ).

thf(1026,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).

thf(297,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).

thf(1167,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( C = B )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(193,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divirors__neq0_0) ).

thf(953,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(306,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).

thf(1185,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(55,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Oadd_0) ).

thf(662,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(78,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__le__imp__le_0) ).

thf(718,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(351,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).

thf(1278,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(267,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__mult__ineq_0) ).

thf(1103,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(324,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__neg__nonpos_0) ).

thf(1219,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(146,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ozero_0) ).

thf(856,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).

thf(93,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).

thf(745,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(363,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(1301,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(65,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).

thf(689,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).

thf(401,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).

thf(1374,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(87,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).

thf(733,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(198,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_RealDef_Oreal__of__preal @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__all__preal_0) ).

thf(965,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_RealDef_Oreal__of__preal @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

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

thf(750,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).

thf(204,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).

thf(975,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(408,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_0) ).

thf(1389,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(106,axiom,
    class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field) ).

thf(772,plain,
    class_RealVector_Oreal__normed__field @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(92,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_even__less__0__iff_1) ).

thf(743,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).

thf(478,axiom,
    class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero) ).

thf(1535,plain,
    class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).

thf(16,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).

thf(545,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(29,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I21_J_0) ).

thf(584,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(290,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__not__less__zero_0) ).

thf(1154,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(140,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono__neg_0) ).

thf(843,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).

thf(277,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__pos_0) ).

thf(1125,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).

thf(186,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__right__mono__neg_0) ).

thf(936,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).

thf(25,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I20_J_0) ).

thf(572,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(76,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).

thf(713,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(332,axiom,
    ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__real__square__gt__zero_1) ).

thf(1239,plain,
    ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).

thf(378,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).

thf(1332,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(262,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__increasing_0) ).

thf(1092,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(261,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).

thf(1090,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(48,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ D @ A ) )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__num__frac_0) ).

thf(641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ D @ A ) )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(426,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).

thf(1428,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(348,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I9_J_0) ).

thf(1271,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(399,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__nonneg_0) ).

thf(1371,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(38,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
       != ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ D @ A )
        = E ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__21_0) ).

thf(611,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
       != ( c_HOL_Oplus__class_Oplus @ C @ E @ A ) )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ D @ A )
        = E ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).

thf(114,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__sum__squares__lt__zero_0) ).

thf(787,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).

thf(177,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ C @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_1) ).

thf(919,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ C @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).

thf(122,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_1) ).

thf(804,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(341,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).

thf(1258,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(72,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_3) ).

thf(704,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(206,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__right_1) ).

thf(979,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).

thf(310,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).

thf(1194,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(168,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__zero__right_0) ).

thf(900,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(473,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__0_0) ).

thf(1524,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(211,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_5) ).

thf(990,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).

thf(482,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ ( c_Polynomial_Opoly @ A @ B @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 @ A @ C ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ B @ tc_Complex_Ocomplex ) @ C @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__bound__exists_1) ).

thf(1542,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ ( c_Polynomial_Opoly @ A @ B @ tc_Complex_Ocomplex ) @ tc_Complex_Ocomplex ) @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 @ A @ C ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ B @ tc_Complex_Ocomplex ) @ C @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(276,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).

thf(1122,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).

thf(499,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).

thf(1574,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(220,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__eq__zero__iff_2) ).

thf(1011,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_2) ).

thf(1048,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(88,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__double__add__iff__zero__le__single__add_1) ).

thf(736,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).

thf(4,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I22_J_0) ).

thf(509,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(236,axiom,
    class_Int_Onumber__ring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

thf(1043,plain,
    class_Int_Onumber__ring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(34,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__idem_0) ).

thf(599,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__idem__mult @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(402,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_0) ).

thf(1376,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(447,axiom,
    class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

thf(1471,plain,
    class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).

thf(255,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).

thf(1080,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).

thf(491,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( B
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).

thf(1557,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( B
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(288,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).

thf(1149,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(43,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__cancel_0) ).

thf(626,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(385,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).

thf(1344,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(104,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_0) ).

thf(769,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(225,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_0) ).

thf(1022,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(301,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__disj_4) ).

thf(1177,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(271,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom) ).

thf(1112,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).

thf(99,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__eq__0__iff_2) ).

thf(758,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(381,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__le__mono_0) ).

thf(1339,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(120,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I10_J_0) ).

thf(799,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(294,axiom,
    class_Ring__and__Field_Oring__no__zero__divisors @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors) ).

thf(1162,plain,
    class_Ring__and__Field_Oring__no__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(82,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).

thf(726,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).

thf(359,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonneg__nonneg_0) ).

thf(1293,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).

thf(57,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__left__commute_0) ).

thf(668,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).

thf(183,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ E @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ D @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__mult__less_0) ).

thf(932,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ E @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ D @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(246,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).

thf(1061,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).

thf(8,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

thf(521,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(449,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right__mono_0) ).

thf(1474,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).

thf(195,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).

thf(959,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).

thf(158,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__neg2_0) ).

thf(883,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).

thf(37,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__semiring__class_Odistrib_0) ).

thf(608,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(209,axiom,
    class_Power_Opower @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).

thf(986,plain,
    class_Power_Opower @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(338,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_4) ).

thf(1250,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(459,axiom,
    class_Ring__and__Field_Oordered__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring) ).

thf(1496,plain,
    class_Ring__and__Field_Oordered__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).

thf(144,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_2) ).

thf(851,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).

thf(1,negated_conjecture,
    c_HOL_Oord__class_Oless @ v_r @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(505,plain,
    c_HOL_Oord__class_Oless @ v_r @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(52,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) @ E @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_combine__common__factor_0) ).

thf(653,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) @ E @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(493,axiom,
    class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).

thf(1562,plain,
    class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(237,axiom,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__norm__iff_0) ).

thf(1044,plain,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).

thf(68,axiom,
    class_Ring__and__Field_Opordered__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring) ).

thf(695,plain,
    class_Ring__and__Field_Opordered__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(335,axiom,
    class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring) ).

thf(1245,plain,
    class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(248,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_2) ).

thf(1066,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(435,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__eq__zero_0) ).

thf(1445,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_RealVector_Onorm__class_Onorm @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(151,axiom,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__zero_0) ).

thf(868,plain,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(272,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).

thf(1113,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(22,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I18_J_0) ).

thf(563,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(215,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).

thf(1000,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).

thf(430,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__mono_0) ).

thf(1435,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_Power_Opower__class_Opower @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(253,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).

thf(1076,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(80,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).

thf(722,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(232,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).

thf(1034,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(504,axiom,
    class_Ring__and__Field_Oordered__field @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field) ).

thf(1583,plain,
    class_Ring__and__Field_Oordered__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(365,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__less__mono2_0) ).

thf(1304,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(318,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__left__neg_0) ).

thf(1208,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(445,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__mono_0) ).

thf(1467,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(17,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
       != ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
      | ( C = E )
      | ( B = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Onoteq__reduce_0) ).

thf(548,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
       != ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) )
      | ( C = E )
      | ( B = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(422,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__order_0) ).

thf(1420,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(181,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonneg__pos_0) ).

thf(927,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(281,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__right_0) ).

thf(1134,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(256,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).

thf(1081,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(40,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__mul__solve_1) ).

thf(617,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).

thf(448,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__right__mono_0) ).

thf(1472,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(97,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).

thf(754,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(118,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_5) ).

thf(795,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(61,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).

thf(680,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(286,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).

thf(1145,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(223,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1_0) ).

thf(1018,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(137,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__1__right_0) ).

thf(836,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(487,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal )
      = ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__assoc_0) ).

thf(1551,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal )
      = ( c_HOL_Otimes__class_Otimes @ A @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).

thf(469,axiom,
    class_OrderedGroup_Opordered__ab__group__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add) ).

thf(1516,plain,
    class_OrderedGroup_Opordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(226,axiom,
    class_Ring__and__Field_Odivision__by__zero @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero) ).

thf(1025,plain,
    class_Ring__and__Field_Odivision__by__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(291,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff2_0) ).

thf(1156,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(327,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__eq__0__iff_1) ).

thf(1225,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__no__zero__divisors @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(339,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).

thf(1252,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).

thf(345,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(1267,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(476,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__mono_0) ).

thf(1531,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Omult__mono @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(329,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_0) ).

thf(1230,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).

thf(485,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__neg__le_1) ).

thf(1547,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__cancel__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(109,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__imp__le_0) ).

thf(776,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(20,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I15_J_0) ).

thf(557,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ E @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(216,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ozero_0) ).

thf(1003,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).

thf(250,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__right__mono_0) ).

thf(1070,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(153,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).

thf(872,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(461,axiom,
    class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors) ).

thf(1499,plain,
    class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).

thf(428,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_0) ).

thf(1432,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).

thf(438,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).

thf(1452,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(116,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).

thf(791,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).

thf(234,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).

thf(1038,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( B = C )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).

thf(343,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__left_1) ).

thf(1262,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(371,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).

thf(1317,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(258,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).

thf(1085,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(124,axiom,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__le__zero__iff_1) ).

thf(808,plain,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(354,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).

thf(1285,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(380,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).

thf(1336,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(171,axiom,
    class_Ring__and__Field_Oordered__ring__strict @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict) ).

thf(907,plain,
    class_Ring__and__Field_Oordered__ring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(415,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( B
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Oadd__r0__iff_1) ).

thf(1404,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( B
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(53,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).

thf(656,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).

thf(325,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).

thf(1221,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(464,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_H_0) ).

thf(1504,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(263,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__mult__pos__le_1) ).

thf(1094,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(218,axiom,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal__of__preal @ A ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__gt__zero__preal__Ex_1) ).

thf(1008,plain,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal__of__preal @ A ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).

thf(147,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero_0) ).

thf(859,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(284,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__cancel__right__disj_3) ).

thf(1141,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(479,axiom,
    class_Ring__and__Field_Omult__zero @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero) ).

thf(1536,plain,
    class_Ring__and__Field_Omult__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(454,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__mono_0) ).

thf(1485,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__semiring @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(241,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).

thf(1052,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(465,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).

thf(1506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(141,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_0) ).

thf(845,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ D @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).

thf(441,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_0) ).

thf(1459,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(303,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).

thf(1180,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(14,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I23_J_0) ).

thf(539,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(488,axiom,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

thf(1553,plain,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(58,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I19_J_0) ).

thf(671,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(373,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__less__iff1_1) ).

thf(1321,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(169,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__cancel__left__neg_0) ).

thf(903,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(418,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_3) ).

thf(1412,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(470,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__ge__zero_0) ).

thf(1517,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(162,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_0) ).

thf(891,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).

thf(436,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).

thf(1448,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(356,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ E @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__le_0) ).

thf(1289,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ E @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(105,axiom,
    class_Ring__and__Field_Osemiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).

thf(771,plain,
    class_Ring__and__Field_Osemiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).

thf(269,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__le__cancel__right_1) ).

thf(1108,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).

thf(9,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).

thf(524,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(28,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Omult__assoc_0) ).

thf(581,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(350,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__nonpos__nonpos_0) ).

thf(1276,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__comm__monoid__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(375,axiom,
    class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero) ).

thf(1326,plain,
    class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(70,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).

thf(699,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(450,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__le__cancel__iff1_0) ).

thf(1476,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(466,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).

thf(1508,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( B = C )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(266,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__less__imp__less__left_0) ).

thf(1101,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ B @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(45,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I24_J_0) ).

thf(632,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(86,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).

thf(731,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).

thf(111,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).

thf(781,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).

thf(213,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__greater_0) ).

thf(995,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(196,axiom,
    ! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 @ A @ B ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_poly__bound__exists_0) ).

thf(961,plain,
    ! [B: $i,A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( v_sko__Fundamental__Theorem__Algebra__Mirabelle__Xpoly__bound__exists__1 @ A @ B ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(126,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).

thf(813,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(406,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__mult__iff_1) ).

thf(1385,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(382,axiom,
    class_Ring__and__Field_Ofield @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).

thf(1341,plain,
    class_Ring__and__Field_Ofield @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(165,axiom,
    class_Power_Opower @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Power_Opower) ).

thf(896,plain,
    class_Power_Opower @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(174,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).

thf(914,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(367,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
       != ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ E @ A )
        = ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).

thf(1308,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
       != ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ E @ A )
        = ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(320,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_0) ).

thf(1212,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(101,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__pos__pos_0) ).

thf(763,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(63,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).

thf(684,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_HOL_Oord__class_Oless @ C @ B @ A )
      | ( C = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).

thf(434,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ozero__left_0) ).

thf(1442,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(13,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Oadd__c_0) ).

thf(536,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(77,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).

thf(716,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).

thf(229,axiom,
    class_Ring__and__Field_Omult__mono1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1) ).

thf(1030,plain,
    class_Ring__and__Field_Omult__mono1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(457,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).

thf(1491,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(432,axiom,
    class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).

thf(1440,plain,
    class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(182,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__le__zero__iff_1) ).

thf(929,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(274,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__le__zero__eq_3) ).

thf(1116,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).

thf(387,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).

thf(1348,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(41,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Oadd_0) ).

thf(620,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(96,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).

thf(752,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_lessequals @ D @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(352,axiom,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__antisym_0) ).

thf(1280,plain,
    ! [B: $i,A: $i] :
      ( ( A = B )
      | ~ ( c_lessequals @ B @ A @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(192,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__eq__0__iff_0) ).

thf(950,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ~ ( class_Ring__and__Field_Omult__zero @ A )
      | ~ ( class_Power_Opower @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).

thf(411,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).

thf(1395,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(129,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal )
       != ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_RealDef_Oreal ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( A = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__right__cancel_0) ).

thf(818,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal )
       != ( c_HOL_Otimes__class_Otimes @ C @ B @ tc_RealDef_Oreal ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( A = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).

thf(404,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__eq__0__iff_1) ).

thf(1380,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(145,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).

thf(854,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(474,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_1) ).

thf(1527,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(337,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).

thf(1248,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).

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

thf(833,plain,
    class_Orderings_Oorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rational_Oordered__idom__class_Osgn__less_0) ).

thf(967,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(149,axiom,
    class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).

thf(865,plain,
    class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(452,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__less__cancel__left_1) ).

thf(1480,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(395,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power_0) ).

thf(1363,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).

thf(2,negated_conjecture,
    c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ v_x @ tc_Complex_Ocomplex ) @ v_r @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(506,plain,
    c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ v_x @ tc_Complex_Ocomplex ) @ v_r @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(243,axiom,
    class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

thf(1056,plain,
    class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).

thf(312,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).

thf(1197,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).

thf(133,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__zero__eq_1) ).

thf(828,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).

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

thf(635,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
        = ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).

thf(69,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_monoid__add__class_Oadd__0__right_0) ).

thf(696,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(79,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1 @ A @ B ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rats__dense__in__nn__real_2) ).

thf(720,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1 @ A @ B ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(386,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__square__less__zero_0) ).

thf(1346,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(160,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( B
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).

thf(886,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( B
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(299,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).

thf(1172,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(166,axiom,
    class_Ring__and__Field_Ocomm__semiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring) ).

thf(897,plain,
    class_Ring__and__Field_Ocomm__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(138,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).

thf(839,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(389,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sum__squares__gt__zero__iff_0) ).

thf(1352,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(279,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Transcendental_Oln @ A )
       != ( c_Transcendental_Oln @ B ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ln__inj__iff_0) ).

thf(1129,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Transcendental_Oln @ A )
       != ( c_Transcendental_Oln @ B ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(480,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).

thf(1537,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(49,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__semigroup__add__class_Oadd__ac_I1_J_0) ).

thf(644,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__semigroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).

thf(392,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_Transcendental_Oln @ A ) @ ( c_Transcendental_Oln @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ln__le__cancel__iff_0) ).

thf(1357,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_Transcendental_Oln @ A ) @ ( c_Transcendental_Oln @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(462,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Oln @ A ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ln__less__self_0) ).

thf(1500,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Oln @ A ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(131,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__0__left_0) ).

thf(822,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).

thf(362,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).

thf(1299,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).

thf(691,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(152,axiom,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict) ).

thf(871,plain,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(413,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ( A = B )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__def_2) ).

thf(1399,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ( A = B )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

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

thf(728,plain,
    class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(90,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__strict__left__mono_0) ).

thf(740,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).

thf(331,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__le__zero__iff_0) ).

thf(1236,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(210,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_no__zero__divisors_0) ).

thf(987,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ono__zero__divisors @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(346,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).

thf(1268,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(26,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A )
        = ( c_HOL_Osgn__class_Osgn @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__sgn_0) ).

thf(575,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ A )
        = ( c_HOL_Osgn__class_Osgn @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(33,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Opwr__mul_0) ).

thf(596,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ B @ D @ A ) @ ( c_Power_Opower__class_Opower @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(403,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1 @ A @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Rats__dense__in__nn__real_1) ).

thf(1378,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_RComplete_Osko__RComplete__XRats__dense__in__nn__real__1__1 @ A @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(172,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__0__0_1) ).

thf(908,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).

thf(212,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).

thf(992,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(179,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__nonpos__nonpos_0) ).

thf(923,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(420,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).

thf(1416,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).

thf(316,axiom,
    class_Int_Onumber__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).

thf(1204,plain,
    class_Int_Onumber__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(74,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__less__iff1_0) ).

thf(708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(397,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__add__le__zero__iff__single__add__le__zero_0) ).

thf(1367,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).

thf(940,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(185,axiom,
    class_OrderedGroup_Omonoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).

thf(935,plain,
    class_OrderedGroup_Omonoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(219,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).

thf(1009,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(443,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__le__0__iff_5) ).

thf(1463,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__ring__strict @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I16_J_0) ).

thf(659,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(495,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__strict__mono_0) ).

thf(1565,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(108,axiom,
    class_Ring__and__Field_Opordered__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring) ).

thf(775,plain,
    class_Ring__and__Field_Opordered__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Osgn__class_Osgn @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sgn__times_0) ).

thf(560,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Osgn__class_Osgn @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Osgn__class_Osgn @ B @ A ) @ ( c_HOL_Osgn__class_Osgn @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(221,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__mult__pos_0) ).

thf(1014,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semiring__strict @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).

thf(202,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(972,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(1584,plain,
    $false,
    inference(e,[status(thm)],[629,1469,1454,1105,1031,893,1179,1295,1549,1369,1190,1315,518,1083,962,1554,1110,1200,977,730,1068,1522,1422,1544,1205,1533,1437,1041,1158,762,614,677,1497,1078,533,1233,1327,1260,945,1063,1354,1164,797,1342,747,1196,898,1576,1441,841,1359,1529,1243,1127,973,885,1046,1228,1482,1287,1430,785,1264,802,1313,1577,934,542,1409,724,587,1323,1511,917,1462,1059,1132,1545,817,638,1147,1319,881,1115,1087,1514,969,1572,1489,1465,789,1450,1373,1334,1151,1383,806,1581,821,905,1302,756,1418,623,1136,834,1183,1283,687,1215,877,956,866,1072,1119,1394,849,507,527,602,981,766,1074,793,925,1306,1199,810,1311,512,942,1057,1163,1274,1387,1519,1255,862,1217,1502,1487,693,815,729,1560,1223,894,825,1343,1021,778,1355,1580,1570,1174,916,1032,1365,879,1555,665,1457,830,889,1210,551,1392,847,566,682,1407,1291,710,1402,1350,1089,1270,1425,1096,1006,1138,593,783,1397,742,578,874,1143,650,948,1567,1493,1329,1160,1028,1361,1292,554,1182,1424,1414,1214,970,706,1016,590,1099,701,1297,738,1539,1192,1050,569,1246,605,647,997,515,1478,984,911,1434,1202,938,1241,921,1563,1170,1035,530,773,765,1054,1187,674,1026,1167,953,1185,662,718,1278,1103,1219,856,745,1301,689,1374,733,965,750,975,1389,772,743,1535,545,584,1154,843,1125,936,572,713,1239,1332,1092,1090,641,1428,1271,1371,611,787,919,804,1258,704,979,1194,900,1524,990,1542,1122,1574,1011,1048,736,509,1043,599,1376,1471,1080,1557,1149,626,1344,769,1022,1177,1112,758,1339,799,1162,726,1293,668,932,1061,521,1474,959,883,608,986,1250,1496,851,505,653,1562,1044,695,1245,1066,1445,868,1113,563,1000,1435,1076,722,1034,1583,1304,1208,1467,548,1420,927,1134,1081,617,1472,754,795,680,1145,1018,836,1551,1516,1025,1156,1225,1252,1267,1531,1230,1547,776,557,1003,1070,872,1499,1432,1452,791,1038,1262,1317,1085,808,1285,1336,907,1404,656,1221,1504,1094,1008,859,1141,1536,1485,1052,1506,845,1459,1180,539,1553,671,1321,903,1412,1517,891,1448,1289,771,1108,524,581,1276,1326,699,1476,1508,1101,632,731,781,995,961,813,1385,1341,896,914,1308,1212,763,684,1442,536,716,1030,1491,1440,929,1116,1348,620,752,1280,950,1395,818,1380,854,1527,1248,833,967,865,1480,1363,506,1056,1197,828,635,696,720,1346,886,1172,897,839,1352,1129,1537,644,1357,1500,822,1299,691,871,1399,728,740,1236,987,1268,575,596,1378,908,992,923,1416,1204,708,1367,940,935,1009,1463,659,1565,775,560,1014,972]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.10  % Problem  : ALG371-1 : TPTP v8.2.0. Released v4.1.0.
% 0.05/0.12  % Command  : run_Leo-III %s %d
% 0.11/0.32  % Computer : n017.cluster.edu
% 0.11/0.32  % Model    : x86_64 x86_64
% 0.11/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32  % Memory   : 8042.1875MB
% 0.11/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32  % CPULimit : 300
% 0.11/0.32  % WCLimit  : 300
% 0.11/0.32  % DateTime : Sat May 18 23:03:09 EDT 2024
% 0.11/0.32  % CPUTime  : 
% 0.91/0.91  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.71/1.21  % [INFO] 	 Parsing done (291ms). 
% 1.71/1.22  % [INFO] 	 Running in sequential loop mode. 
% 2.62/1.57  % [INFO] 	 eprover registered as external prover. 
% 2.62/1.57  % [INFO] 	 cvc4 registered as external prover. 
% 2.62/1.58  % [INFO] 	 Scanning for conjecture ... 
% 2.92/1.74  % [INFO] 	 Found a conjecture (or negated_conjecture) and 501 axioms. Running axiom selection ... 
% 3.49/1.90  % [INFO] 	 Axiom selection finished. Selected 501 axioms (removed 0 axioms). 
% 4.48/2.13  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.48/2.15  % [INFO] 	 Type checking passed. 
% 4.61/2.15  % [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 ... 
% 12.72/4.31  % External prover 'e' found a proof!
% 12.72/4.31  % [INFO] 	 Killing All external provers ... 
% 12.72/4.32  % Time passed: 3856ms (effective reasoning time: 3090ms)
% 12.72/4.32  % Axioms used in derivation (501): cls_mult__less__cancel__left__disj_5, cls_add__0__left_0, cls_xt1_I9_J_0, cls_le__divide__eq_8, cls_linorder__antisym__conv2_1, cls_add__pos__nonneg_0, cls_divide__eq__eq_3, cls_le__divide__eq_3, cls_order__le__less__trans_0, cls_mult__zero__right_0, cls_less__divide__eq_3, cls_divide__le__eq_2, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_divide__less__0__iff_0, cls_comm__semiring__class_Odistrib_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_zero__less__divide__iff_5, cls_real__mult__le__cancel__iff1_0, cls_divide__pos__pos_0, cls_mult__imp__le__div__pos_0, clsarity_RealDef__Oreal__Orderings_Opreorder, cls_class__ringb_Oadd__r0__iff_1, cls_mult__nonneg__nonneg_0, clsarity_RealDef__Oreal__Ring__and__Field_Ozero__neq__one, cls_add__less__cancel__left_1, cls_mult__right__mono_0, cls_mult__right_Ozero_0, cls_real__mult__assoc_0, cls_xt1_I12_J_0, cls_mult__less__cancel__right__disj_0, cls_mult__nonneg__nonpos2_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_sgn__times_0, cls_real__mult__le__cancel__iff2_1, cls_mult__less__cancel__left__disj_1, cls_norm__zero_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors, cls_real__less__def_1, cls_sum__squares__eq__zero__iff_0, cls_zero__less__norm__iff_1, cls_divide__nonpos__neg_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_add__increasing2_0, cls_zero__le__mult__iff_3, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring, cls_not__sum__squares__lt__zero_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_pos__add__strict_0, cls_zero__le__divide__iff_2, cls_linorder__neqE_0, cls_add__strict__right__mono_0, cls_power__le__zero__eq_3, cls_class__semiring_Osemiring__rules_I21_J_0, cls_sgn0_0, cls_divide__less__eq_4, cls_zero__less__divide__iff_0, cls_Rational_Oordered__idom__class_Osgn__greater_1, clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add, cls_class__semiring_Osemiring__rules_I10_J_0, cls_add__imp__eq_0, cls_divide__le__eq_7, cls_real__mult__less__iff1_0, cls_frac__le_0, cls_add__le__cancel__right_1, cls_add__le__cancel__left_1, cls_divide__le__eq_8, cls_real__le__trans_0, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field, clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add, cls_mult__nonpos__nonneg_0, cls_power__less__zero__eq_1, cls_divide__eq__eq_0, cls_mult__nonpos__nonpos_0, cls_class__ringb_Onoteq__reduce_0, cls_comm__monoid__add_Omult__1__right_0, cls_sum__squares__ge__zero_0, cls_add__nonpos__neg_0, cls_mult__less__imp__less__right_0, cls_comm__monoid__add_Omult__assoc_0, cls_order__less__trans_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_divide__less__eq_5, cls_add__cancel__21_1, cls_real__mult__le__cancel__iff2_0, cls_add__left__cancel_0, cls_mult__le__cancel__left__pos_0, cls_split__mult__neg__le_0, cls_divide__le__0__iff_3, cls_mult__less__imp__less__left_0, cls_sum__squares__le__zero__iff_1, cls_sgn__zero_0, cls_less__divide__eq_4, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult, cls_mult__eq__0__iff_0, cls_add__nonneg__pos_0, cls_divide__strict__left__mono_0, cls_mult__less__cancel__left__disj_4, cls_class__ringb_Oadd__mul__solve_1, cls_mult__less__cancel__right__disj_3, clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_frac__eq__eq_0, cls_divide__eq__eq_4, cls_mult__left__mono__neg_0, cls_add__right__mono_0, cls_mult_Ozero__left_0, cls_divide__neg__neg_0, cls_eq__divide__eq_4, cls_mult__mono_0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult, cls_zero__less__double__add__iff__zero__less__single__add_0, cls_class__semiring_Omul__0_0, cls_field__power__not__zero_0, cls_poly__bound__exists_1, cls_order__less__asym_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_linorder__not__less_0, cls_double__add__less__zero__iff__single__less__zero_0, cls_zero__le__mult__iff_0, cls_order__le__less_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, clsarity_RealDef__Oreal__RealVector_Oreal__normed__div__algebra, cls_real__le__linear_0, cls_mult__strict__right__mono_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors, cls_class__semiring_Omul__c_0, cls_mult__pos__neg_0, cls_order__eq__refl_0, cls_mult__strict__mono_0, clsarity_Complex__Ocomplex__Ring__and__Field_Omult__zero, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1, cls_mult_Ozero__right_0, cls_mult__left__mono_0, cls_divide__strict__left__mono__neg_0, cls_linorder__antisym__conv1_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero, cls_mult_Oadd__left_0, cls_linorder__antisym__conv2_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero, cls_mult__right_Oadd_0, cls_divide__left__mono__neg_0, cls_real__less__def_0, cls_less__divide__eq_7, cls_le__divide__eq_7, cls_divide__right__mono_0, cls_divide__right__mono__neg_0, cls_xt1_I10_J_0, cls_add__nonneg__eq__0__iff_0, cls_le__divide__eq_2, cls_add__divide__distrib_0, cls_divide__le__eq_3, cls_not__less__iff__gr__or__eq_0, cls_no__zero__divisors_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict, cls_mult__frac__num_0, cls_zero__le__mult__iff_4, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_less__le__not__le_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_divide__neg__pos_0, clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero, cls_add__left__mono_0, cls_norm__ge__zero_0, cls_add__less__cancel__right_1, cls_divide__less__eq_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_mult__frac__frac_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_norm__sgn_0, cls_add__strict__left__mono_0, cls_sgn__0__0_0, cls_less__divide__eq_2, cls_Rational_Oordered__idom__class_Osgn__less_0, cls_ln__less__cancel__iff_1, cls_real__le__refl_0, cls_mult__neg__pos_0, cls_norm__not__less__zero_0, cls_combine__common__factor_0, cls_zero__less__divide__iff_1, cls_mult__le__0__iff_0, cls_add__le__less__mono_0, cls_mult__right__le__imp__le_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring, cls_zero__le__divide__iff_3, cls_class__ringb_Onoteq__reduce_1, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add, cls_sgn__0__0_1, cls_real__mult__less__mono2_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add, cls_mult__pos__neg2_0, clsarity_RealDef__Oreal__Orderings_Olinorder, cls_class__semiring_Osemiring__rules_I15_J_0, cls_mult__mono1_0, cls_mult__less__cancel__left__disj_0, cls_class__semiring_Oadd__a_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_class__semiring_Osemiring__rules_I19_J_0, cls_xt1_I8_J_0, cls_eq__divide__eq_0, cls_mult__le__cancel__left__pos_1, cls_mult__le__cancel__left__neg_1, cls_eq__divide__eq_3, cls_class__semiring_Oadd__0_0, cls_mult__imp__div__pos__le_0, cls_class__semiring_Osemiring__rules_I16_J_0, cls_mult__left__idem_0, cls_add__right__cancel_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra, cls_mult__le__0__iff_1, cls_zero__less__mult__pos_0, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add, cls_class__semiring_Osemiring__rules_I1_J_0, cls_split__mult__pos__le_0, cls_sum__squares__le__zero__iff_2, cls_divide_Ozero_0, cls_divide__self__if_0, cls_zero__le__power__iff_1, cls_class__semiring_Osemiring__rules_I17_J_0, cls_comm__monoid__add_Omult__commute_0, clsarity_RealDef__Oreal__Power_Opower, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add, cls_mult__le__0__iff_4, cls_linorder__linear_0, cls_real__mult__less__iff1_1, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict, cls_class__ringb_Oadd__mul__solve_0, cls_add__strict__mono_0, cls_sum__squares__eq__zero__iff_1, cls_zero__le__divide__iff_5, cls_divide__less__0__iff_3, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1, cls_not__leE_0, cls_divide__less__eq_8, cls_mult__less__cancel__right__disj_2, cls_zero__less__power_0, cls_sgn__zero__iff_0, cls_add__cancel__21_0, cls_order__trans_0, cls_divide__nonneg__neg_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, cls_power__divide_0, cls_mult__strict__left__mono_0, cls_sum__squares__gt__zero__iff_2, cls_divide__le__0__iff_2, cls_class__semiring_Omul__d_0, cls_real__mult__order_0, cls_order__antisym_0, cls_divide__le__eq_6, cls_divide__less__eq_1, cls_mult__left__less__imp__less_0, cls_linorder__antisym__conv1_1, cls_split__mult__pos__le_1, cls_real__gt__zero__preal__Ex_1, cls_real__mult__left__cancel_0, cls_add__frac__eq_0, cls_no__zero__divirors__neq0_0, cls_mult__le__0__iff_5, clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add, cls_add__num__frac_0, cls_mult__strict__mono_H_0, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_less__divide__eq_5, cls_ln__less__cancel__iff_0, cls_less__divide__eq_8, cls_divide__le__eq_0, cls_zero__less__divide__iff_3, clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector, cls_ln__less__self_0, cls_zero__le__divide__iff_4, cls_real__mult__right__cancel_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add, cls_Rational_Oordered__idom__class_Osgn__less_1, clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add, clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult, cls_divide__nonneg__pos_0, cls_mult__less__cancel__right__disj_5, clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one, cls_real__less__all__preal_0, cls_divide__le__0__iff_5, cls_linorder__not__le_1, cls_add__less__cancel__right_0, cls_divide__zero_0, cls_divide__le__eq_4, cls_class__semiring_Omul__a_0, cls_not__less__iff__gr__or__eq_1, cls_zero__le__square_0, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_add__increasing_0, cls_class__ringb_Oadd__scale__eq__noteq_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oidom, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add, cls_order__le__neq__trans_0, cls_real__of__preal__zero__less_0, cls_mult__nonneg__nonpos_0, cls_class__semiring_Osemiring__rules_I23_J_0, cls_less__divide__eq_1, cls_zero__less__divide__iff_2, clsarity_RealDef__Oreal__Ring__and__Field_Oidom, cls_mult__imp__less__div__pos_0, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_le__divide__eq_6, cls_class__ringb_Oadd__cancel_0, cls_add__nonpos__nonpos_0, cls_divide__pos__neg_0, cls_less__le__not__le_1, cls_add__nonneg__eq__0__iff_1, cls_le__divide__eq_1, cls_divide__le__0__iff_1, cls_mult__eq__0__iff_2, cls_Rats__dense__in__nn__real_1, cls_order__eq__iff_2, cls_not__square__less__zero_0, cls_linorder__antisym__conv3_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add, cls_le__divide__eq_0, cls_divide__zero__left_0, cls_linorder__neqE__ordered__idom_0, cls_order__neq__le__trans_0, cls_add__nonneg__nonneg_0, cls_mult__mono_H_0, cls_mult__strict__left__mono__comm_0, cls_class__ringb_Oadd__r0__iff_0, cls_mult__less__cancel__left__neg_1, cls_order__antisym__conv_0, cls_even__less__0__iff_1, cls_sum__squares__gt__zero__iff_1, cls_eq__divide__eq_2, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_add__strict__increasing_0, cls_divide__less__eq_2, cls_not__real__square__gt__zero_1, cls_linorder__less__linear_0, cls_power__mult__distrib_0, cls_eq__divide__imp_0, clsarity_RealDef__Oreal__Ring__and__Field_Ofield, cls_order__less__le_2, cls_divide__strict__right__mono__neg_0, cls_mult__less__cancel__left__pos_1, cls_zero__le__mult__iff_5, cls_divide__le__eq_5, cls_ln__inj__iff_0, cls_zero__le__mult__iff_1, cls_power__commutes_0, cls_xt1_I11_J_0, cls_add__neg__neg_0, cls_mult__imp__div__pos__less_0, cls_double__eq__0__iff_0, cls_mult__le__0__iff_2, cls_norm__mult_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__field, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector, cls_divide__eq__imp_0, cls_mult__le__cancel__left__neg_0, cls_divide__less__eq_7, cls_zero__le__divide__iff_0, cls_norm__eq__zero_0, cls_class__semiring_Osemiring__rules_I18_J_0, cls_sum__squares__eq__zero__iff_2, cls_real__le__antisym_0, cls_divide__less__0__iff_2, cls_xt1_I6_J_0, cls_le__add__right__mono_0, cls_zero__less__mult__pos2_0, cls_divide__left__mono_0, cls_mult_Oadd__right_0, cls_divide__less__0__iff_5, clsarity_RealDef__Oreal__Ring__and__Field_Osemiring, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add, cls_comm__monoid__add_Omult__left__commute_0, cls_add__frac__num_0, cls_mult__right__mono__neg_0, cls_sgn__sgn_0, cls_mult__less__cancel__left__disj_3, cls_norm__mult__ineq_0, cls_mult__less__cancel__right__disj_4, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add, cls_comm__monoid__add_Omult__1_0, cls_frac__eq__eq_1, cls_divide__le__0__iff_4, cls_norm__le__zero__iff_1, cls_linorder__not__le_0, cls_double__add__less__zero__iff__single__less__zero_1, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors, cls_Rational_Oordered__idom__class_Osgn__greater_0, cls_mult__zero__left_0, cls_norm__mult__less_0, cls_le__divide__eq_9, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult, cls_frac__less2_0, cls_add__nonneg__eq__0__iff_2, cls_le__divide__eq_4, cls_power__eq__0__iff_0, cls_class__semiring_Oadd__c_0, cls_less__divide__eq_6, cls_nonzero__power__divide_0, cls_mult__pos__pos_0, cls_mult__left__le__imp__le_0, cls_mult__strict__right__mono__neg_0, cls_divide__less__0__iff_1, cls_order__less__irrefl_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__field, cls_add__pos__pos_0, cls_add__mono_0, cls_divide_Oadd_0, cls_mult__right__less__imp__less_0, cls_ln__le__cancel__iff_0, cls_sum__squares__gt__zero__iff_0, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring, cls_class__semiring_Osemiring__rules_I8_J_0, cls_sgn__mult_0, cls_norm__ratiotest__lemma_0, cls_zero__less__divide__iff_4, cls_power__less__imp__less__base_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom, cls_divide__le__0__iff_0, cls_real__less__all__real2_0, cls_divide__less__eq_9, cls_add__neg__nonpos_0, clsarity_Complex__Ocomplex__Power_Opower, cls_mult__divide__mult__cancel__right_0, cls_mult__less__cancel__left__disj_2, cls_class__semiring_Opwr__mul_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_mult__less__cancel__right__disj_1, cls_divide__le__eq_9, cls_Rats__dense__in__nn__real_2, clsarity_RealDef__Oreal__Orderings_Oorder, cls_add__less__cancel__left_0, cls_divide__strict__right__mono_0, cls_divide__less__eq_6, cls_frac__less_0, cls_real__mult__commute_0, clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult, cls_real__mult__le__cancel__iff1_1, cls_class__semiring_Osemiring__rules_I25_J_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring, cls_mult__eq__0__iff_1, cls_zero__le__power_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, cls_less__divide__eq_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring, cls_order__less__imp__le_0, cls_real__less__def_2, cls_not__real__square__gt__zero_0, cls_divide__nonpos__pos_0, cls_add__less__le__mono_0, clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add, cls_norm__le__zero__iff_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom, cls_divide__less__eq_3, cls_zero__le__divide__iff_1, clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors, cls_zero__less__norm__iff_0, cls_monoid__add__class_Oadd__0__right_0, cls_mult__idem_0, cls_add__strict__increasing2_0, clsarity_RealDef__Oreal__Int_Onumber__ring, clsarity_RealDef__Oreal__Ring__and__Field_Osgn__if, cls_divide__eq__eq_1, cls_le__divide__eq_5, cls_xt1_I7_J_0, cls_mult__less__le__imp__less_0, clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors, cls_mult__divide__mult__cancel__left_0, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, cls_ln__le__cancel__iff_1, cls_less__divide__eq_9, cls_order__less__le_1, cls_mult__le__0__iff_3, cls_mult__neg__neg_0, cls_linorder__not__less_1, cls_mult__less__cancel__left__neg_0, clsarity_Complex__Ocomplex__Int_Onumber__ring, cls_add__le__cancel__left_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring, cls_even__less__0__iff_0, cls_mult__left_Oadd_0, cls_sum__squares__le__zero__iff_0, cls_add__le__cancel__right_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, cls_mult__less__cancel__left__pos_0, cls_divide__less__0__iff_4, cls_split__mult__neg__le_1, cls_class__semiring_Osemiring__rules_I22_J_0, cls_poly__bound__exists_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict, cls_power__mono_0, cls_zero__le__mult__iff_2, cls_divide__le__eq_1, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__strict__left__mono__neg_0
% 12.72/4.32  % No. of inferences in proof: 1009
% 12.72/4.32  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3856 ms resp. 3090 ms w/o parsing
% 14.12/4.59  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.12/4.60  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------