TSTP Solution File: ALG406-1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : ALG406-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n008.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 18:15:23 EDT 2024

% Result   : Unsatisfiable 60.98s 12.38s
% Output   : Refutation 61.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      :  768
% Syntax   : Number of formulae    : 1447 ( 289 unt;  90 typ;   0 def)
%            Number of atoms       : 3525 ( 644 equ;   0 cnn)
%            Maximal formula atoms :    6 (   2 avg)
%            Number of connectives : 16974 (2064   ~;2168   |;   0   &;12742   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   8 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  109 ( 109   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   92 (  90 usr;   6 con; 0-3 aty)
%            Number of variables   : 2982 (   0   ^2982   !;   0   ?;2982   :)

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

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

thf(v_t_____type,type,
    v_t____: $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_OrderedGroup_Ocancel__semigroup__add_type,type,
    class_OrderedGroup_Ocancel__semigroup__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_Ring__and__Field_Oordered__semidom_type,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(c_NthRoot_Osqrt_type,type,
    c_NthRoot_Osqrt: $i > $i ).

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

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

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

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

thf(class_OrderedGroup_Olordered__ab__group__add__abs_type,type,
    class_OrderedGroup_Olordered__ab__group__add__abs: $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_Ring__and__Field_Omult__mono1_type,type,
    class_Ring__and__Field_Omult__mono1: $i > $o ).

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

thf(class_Ring__and__Field_Oabs__if_type,type,
    class_Ring__and__Field_Oabs__if: $i > $o ).

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

thf(class_RealVector_Oreal__algebra__1_type,type,
    class_RealVector_Oreal__algebra__1: $i > $o ).

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

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

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

thf(c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1_type,type,
    c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1: $i > $i > $i ).

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

thf(c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1_type,type,
    c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1: $i > $i > $i ).

thf(c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1_type,type,
    c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1: $i > $i > $i ).

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

thf(c_Transcendental_Osin_type,type,
    c_Transcendental_Osin: $i > $i ).

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

thf(c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1_type,type,
    c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1: $i > $i > $i ).

thf(c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1_type,type,
    c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1: $i > $i > $i ).

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_Olordered__ring_type,type,
    class_Ring__and__Field_Olordered__ring: $i > $o ).

thf(c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1_type,type,
    c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1: $i > $i > $i ).

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

thf(c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1_type,type,
    c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1: $i > $i > $i ).

thf(c_Transcendental_Ocos_type,type,
    c_Transcendental_Ocos: $i > $i ).

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

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

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

thf(c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1_type,type,
    c_RealVector_Osko__RealVector__Xmult__left__Xbounded__1__1: $i > $i > $i ).

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

thf(c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1_type,type,
    c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1: $i > $i > $i ).

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

thf(444,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(1665,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)],[444]) ).

thf(354,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(1469,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)],[354]) ).

thf(519,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_1) ).

thf(1823,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(604,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__one_0) ).

thf(1995,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(244,axiom,
    ( ( c_Transcendental_Osin @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__zero_0) ).

thf(1237,plain,
    ( ( c_Transcendental_Osin @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(106,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__minus__eq_0) ).

thf(909,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).

thf(100,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_0) ).

thf(893,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).

thf(599,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(1982,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)],[599]) ).

thf(118,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__imp__less_0) ).

thf(941,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(583,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(1950,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)],[583]) ).

thf(395,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(1554,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)],[395]) ).

thf(651,axiom,
    ! [A: $i] :
      ( ( ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal )
       != ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__is__one_0) ).

thf(2094,plain,
    ! [A: $i] :
      ( ( ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal )
       != ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(329,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(1411,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)],[329]) ).

thf(671,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__imp__le_0) ).

thf(2131,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(347,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__minus__cancel_0) ).

thf(1454,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ( ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_RealVector_Onorm__class_Onorm @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).

thf(642,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ 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_abs__eq__mult_3) ).

thf(2072,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ 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)],[642]) ).

thf(492,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Oone__class_Oone @ 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__right__le__one__le_0) ).

thf(1767,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Oone__class_Oone @ 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)],[492]) ).

thf(397,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(1559,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)],[397]) ).

thf(182,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__imp__positive_0) ).

thf(1105,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).

thf(283,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(1315,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)],[283]) ).

thf(533,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(1850,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).

thf(644,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(2077,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)],[644]) ).

thf(208,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(1158,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).

thf(664,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__power_0) ).

thf(2117,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(4,axiom,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring__strict) ).

thf(683,plain,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).

thf(168,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_1) ).

thf(1068,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).

thf(380,axiom,
    ( ( c_NthRoot_Osqrt @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__zero_0) ).

thf(1522,plain,
    ( ( c_NthRoot_Osqrt @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).

thf(638,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(2062,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)],[638]) ).

thf(139,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
        = ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__power__inverse_0) ).

thf(994,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
        = ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).

thf(578,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(1939,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)],[578]) ).

thf(170,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).

thf(1073,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).

thf(613,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_division__ring__inverse__add_0) ).

thf(2014,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(230,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(1205,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)],[230]) ).

thf(593,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(1971,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)],[593]) ).

thf(363,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).

thf(1486,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(37,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_1) ).

thf(730,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).

thf(271,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(1290,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)],[271]) ).

thf(341,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(1443,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)],[341]) ).

thf(511,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__0__iff_0) ).

thf(1808,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(662,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__iff_2) ).

thf(2114,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(260,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__minus__self_0) ).

thf(1269,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(447,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(1671,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)],[447]) ).

thf(486,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__le__zero_0) ).

thf(1756,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(624,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__minus__mult__self__le_0) ).

thf(2035,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(32,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( B
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).

thf(715,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( B
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).

thf(242,axiom,
    ! [D: $i,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_HOL_Otimes__class_Otimes @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 @ D @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ononneg__bounded_1) ).

thf(1233,plain,
    ! [D: $i,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_HOL_Otimes__class_Otimes @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 @ D @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).

thf(19,axiom,
    class_Ring__and__Field_Osemiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

thf(698,plain,
    class_Ring__and__Field_Osemiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(488,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_0) ).

thf(1761,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).

thf(585,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(1954,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).

thf(237,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(1222,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)],[237]) ).

thf(369,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(1497,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)],[369]) ).

thf(463,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(1705,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)],[463]) ).

thf(172,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(1078,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)],[172]) ).

thf(501,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(1788,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(335,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(1426,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)],[335]) ).

thf(606,axiom,
    class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1) ).

thf(1999,plain,
    class_RealVector_Oreal__normed__algebra__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(62,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( B
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).

thf(797,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( B
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).

thf(263,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(1275,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)],[263]) ).

thf(676,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(2141,plain,
    class_RealVector_Oreal__normed__div__algebra @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(568,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(1919,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)],[568]) ).

thf(601,axiom,
    ! [D: $i,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_HOL_Otimes__class_Otimes @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 @ D @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Opos__bounded_1) ).

thf(1988,plain,
    ! [D: $i,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_HOL_Otimes__class_Otimes @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 @ D @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(226,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I11_J_0) ).

thf(1196,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(102,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).

thf(898,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).

thf(142,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oabs__if @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_0) ).

thf(1001,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oabs__if @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).

thf(192,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(1127,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)],[192]) ).

thf(405,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(1576,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(30,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(709,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)],[30]) ).

thf(131,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(973,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)],[131]) ).

thf(569,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(1921,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)],[569]) ).

thf(304,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_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 @ C @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Opos__bounded_1) ).

thf(1359,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_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 @ C @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(309,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(1366,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)],[309]) ).

thf(553,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(1887,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)],[553]) ).

thf(74,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
       != ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_0) ).

thf(829,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
       != ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(178,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__cancel_0) ).

thf(1095,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).

thf(472,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__two_0) ).

thf(1724,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(358,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(1475,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)],[358]) ).

thf(640,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(2067,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)],[640]) ).

thf(383,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(1529,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)],[383]) ).

thf(561,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(1904,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(378,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ominus_0) ).

thf(1518,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).

thf(258,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ ( c_RealVector_Onorm__class_Onorm @ A @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__mod__minus__le__complex__mod_0) ).

thf(1265,plain,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ ( c_RealVector_Onorm__class_Onorm @ A @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ A @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).

thf(462,axiom,
    ! [A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__0__iff_0) ).

thf(1703,plain,
    ! [A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(361,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(1482,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)],[361]) ).

thf(252,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(1254,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)],[252]) ).

thf(427,axiom,
    class_OrderedGroup_Opordered__ab__group__add__abs @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs) ).

thf(1628,plain,
    class_OrderedGroup_Opordered__ab__group__add__abs @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(35,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(724,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)],[35]) ).

thf(503,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__mult_0) ).

thf(1792,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Olordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(600,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
       != ( c_HOL_Oone__class_Oone @ A ) )
      | ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__unique_0) ).

thf(1985,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
       != ( c_HOL_Oone__class_Oone @ A ) )
      | ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(627,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(2039,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)],[627]) ).

thf(544,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(1871,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)],[544]) ).

thf(563,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
       != ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__neq__one_0) ).

thf(1907,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
       != ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(288,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(1323,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)],[288]) ).

thf(64,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(802,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)],[64]) ).

thf(521,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(1826,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)],[521]) ).

thf(406,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
        = ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__pos_0) ).

thf(1577,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
        = ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(603,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(1992,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)],[603]) ).

thf(669,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__add_0) ).

thf(2126,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(350,axiom,
    class_Ring__and__Field_Opordered__ring__abs @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs) ).

thf(1462,plain,
    class_Ring__and__Field_Opordered__ring__abs @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).

thf(121,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__inverse__less__neg_0) ).

thf(949,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).

thf(291,axiom,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__0_0) ).

thf(1330,plain,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).

thf(539,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(1860,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)],[539]) ).

thf(257,axiom,
    class_Orderings_Oorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).

thf(1264,plain,
    class_Orderings_Oorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).

thf(375,axiom,
    ! [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_Oinverse @ 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_inverse__nonpositive__iff__nonpositive_1) ).

thf(1511,plain,
    ! [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_Oinverse @ 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)],[375]) ).

thf(109,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(917,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)],[109]) ).

thf(23,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(702,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).

thf(282,axiom,
    ! [D: $i,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_HOL_Otimes__class_Otimes @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1 @ D @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Obounded_0) ).

thf(1313,plain,
    ! [D: $i,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_HOL_Otimes__class_Otimes @ ( c_RealVector_Onorm__class_Onorm @ B @ A ) @ ( c_RealVector_Onorm__class_Onorm @ C @ A ) @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__Xbounded__1__1 @ D @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).

thf(265,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).

thf(1279,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).

thf(524,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(1832,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)],[524]) ).

thf(223,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(1191,plain,
    class_Ring__and__Field_Ozero__neq__one @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).

thf(314,axiom,
    ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__is__one_1) ).

thf(1379,plain,
    ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).

thf(175,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_0) ).

thf(1087,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).

thf(632,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(2049,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)],[632]) ).

thf(419,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__right_0) ).

thf(1609,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(52,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__0__iff__less_0) ).

thf(770,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(186,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(1115,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)],[186]) ).

thf(402,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(1568,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)],[402]) ).

thf(434,axiom,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ 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__sqrt__le__0__iff_1) ).

thf(1641,plain,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ 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)],[434]) ).

thf(515,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(1815,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)],[515]) ).

thf(306,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq_0) ).

thf(1362,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).

thf(547,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(1875,plain,
    class_RealVector_Oreal__normed__div__algebra @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(241,axiom,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__refl_0) ).

thf(1232,plain,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).

thf(365,axiom,
    class_Int_Onumber__ring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Int_Onumber__ring) ).

thf(1489,plain,
    class_Int_Onumber__ring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).

thf(112,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__cancel_0) ).

thf(924,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(59,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_1) ).

thf(789,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).

thf(312,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(1373,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)],[312]) ).

thf(293,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult) ).

thf(1334,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).

thf(205,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(1151,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)],[205]) ).

thf(588,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(1960,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)],[588]) ).

thf(128,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_2) ).

thf(966,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).

thf(71,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_0) ).

thf(821,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).

thf(614,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(2017,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)],[614]) ).

thf(276,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(1302,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)],[276]) ).

thf(47,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(756,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)],[47]) ).

thf(443,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).

thf(1664,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(656,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(2105,plain,
    class_Ring__and__Field_Odivision__by__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(345,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal )
       != ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_1) ).

thf(1450,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal )
       != ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).

thf(157,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero_0) ).

thf(1040,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).

thf(429,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(1632,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)],[429]) ).

thf(196,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left__le__one__le_0) ).

thf(1136,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).

thf(76,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__left__minus_0) ).

thf(834,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).

thf(538,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D1_0) ).

thf(1858,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).

thf(667,axiom,
    ! [A: $i] :
      ( ( ( c_NthRoot_Osqrt @ A )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__0__iff_0) ).

thf(2122,plain,
    ! [A: $i] :
      ( ( ( c_NthRoot_Osqrt @ A )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(522,axiom,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__1__iff_0) ).

thf(1828,plain,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).

thf(597,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(1978,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)],[597]) ).

thf(51,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_NthRoot_Osqrt @ A )
       != ( c_NthRoot_Osqrt @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__iff_0) ).

thf(766,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_NthRoot_Osqrt @ A )
       != ( c_NthRoot_Osqrt @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).

thf(572,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_Ouminus__class_Ouminus @ B @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_0) ).

thf(1928,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_Ouminus__class_Ouminus @ B @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).

thf(234,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(1215,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)],[234]) ).

thf(88,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(866,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)],[88]) ).

thf(505,axiom,
    ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__is__one_2) ).

thf(1796,plain,
    ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).

thf(321,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(1394,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).

thf(300,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__zero_0) ).

thf(1351,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).

thf(580,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__1__mult_0) ).

thf(1943,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).

thf(246,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(1242,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)],[246]) ).

thf(379,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).

thf(1521,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(459,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(1696,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)],[459]) ).

thf(400,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(1564,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)],[400]) ).

thf(212,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_1) ).

thf(1169,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).

thf(8,axiom,
    class_Ring__and__Field_Ozero__neq__one @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ozero__neq__one) ).

thf(687,plain,
    class_Ring__and__Field_Ozero__neq__one @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).

thf(557,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(1896,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)],[557]) ).

thf(13,axiom,
    class_Power_Opower @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Power_Opower) ).

thf(692,plain,
    class_Power_Opower @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).

thf(344,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(1447,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)],[344]) ).

thf(124,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
        = ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__inverse_0) ).

thf(956,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
        = ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).

thf(382,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(1526,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)],[382]) ).

thf(674,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_1) ).

thf(2137,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(655,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(2103,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)],[655]) ).

thf(326,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(1405,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)],[326]) ).

thf(541,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(1863,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(438,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(1651,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)],[438]) ).

thf(417,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I4_J_0) ).

thf(1604,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ B @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(612,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(2011,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)],[612]) ).

thf(457,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(1691,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)],[457]) ).

thf(339,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(1438,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)],[339]) ).

thf(278,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(1306,plain,
    class_Ring__and__Field_Oordered__idom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).

thf(227,axiom,
    ! [A: $i] :
      ( ( ( c_NthRoot_Osqrt @ A )
       != ( c_HOL_Ozero__class_Ozero @ 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__sqrt__not__eq__zero_0) ).

thf(1199,plain,
    ! [A: $i] :
      ( ( ( c_NthRoot_Osqrt @ A )
       != ( c_HOL_Ozero__class_Ozero @ 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)],[227]) ).

thf(49,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(761,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)],[49]) ).

thf(67,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(810,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)],[67]) ).

thf(295,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(1338,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)],[295]) ).

thf(631,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 @ C @ A ) @ ( c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Opos__bounded_1) ).

thf(2047,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 @ C @ A ) @ ( c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(499,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(1783,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)],[499]) ).

thf(478,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(1736,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)],[478]) ).

thf(543,axiom,
    ! [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 @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I2_J_0) ).

thf(1868,plain,
    ! [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 @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(607,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(2000,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)],[607]) ).

thf(475,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(1730,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)],[475]) ).

thf(566,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(1915,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)],[566]) ).

thf(465,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(1708,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)],[465]) ).

thf(43,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__minus__cancel_0) ).

thf(746,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).

thf(190,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(1123,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)],[190]) ).

thf(235,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(1217,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)],[235]) ).

thf(14,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(693,plain,
    class_Orderings_Oorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).

thf(622,axiom,
    class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add) ).

thf(2032,plain,
    class_OrderedGroup_Ogroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(551,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(1883,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)],[551]) ).

thf(317,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Opos__bounded_0) ).

thf(1387,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__Xpos__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(559,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(1900,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)],[559]) ).

thf(149,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ 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_negative__imp__inverse__negative_0) ).

thf(1021,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ 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)],[149]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
       != ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
      | ( B = C )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__eq__imp__eq_0) ).

thf(778,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
       != ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
      | ( B = C )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(302,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(1355,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)],[302]) ).

thf(407,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(1580,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)],[407]) ).

thf(403,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(1570,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)],[403]) ).

thf(215,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(1174,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)],[215]) ).

thf(449,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(1676,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)],[449]) ).

thf(672,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(2133,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)],[672]) ).

thf(371,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(1502,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)],[371]) ).

thf(484,axiom,
    ! [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_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_2) ).

thf(1751,plain,
    ! [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_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(423,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(1619,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)],[423]) ).

thf(311,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(1370,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)],[311]) ).

thf(334,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1_0) ).

thf(1423,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocomm__monoid__mult @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).

thf(577,axiom,
    class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring) ).

thf(1938,plain,
    class_Ring__and__Field_Oring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(308,axiom,
    class_OrderedGroup_Omonoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).

thf(1365,plain,
    class_OrderedGroup_Omonoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).

thf(93,axiom,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict) ).

thf(879,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).

thf(83,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_1) ).

thf(852,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ B @ A ) @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).

thf(217,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__ge__self_0) ).

thf(1178,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).

thf(209,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(1159,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)],[209]) ).

thf(526,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_field__inverse_0) ).

thf(1836,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).

thf(440,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonpos_0) ).

thf(1656,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(266,axiom,
    c_HOL_Oord__class_Oless @ v_t____ @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_t_I2_J_0) ).

thf(1281,plain,
    c_HOL_Oord__class_Oless @ v_t____ @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(660,axiom,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector) ).

thf(2112,plain,
    class_RealVector_Oreal__normed__vector @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(404,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__left_0) ).

thf(1573,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(146,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(1012,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)],[146]) ).

thf(154,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus_0) ).

thf(1032,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(416,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(1602,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)],[416]) ).

thf(455,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
       != ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
      | ( B
        = ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_0) ).

thf(1687,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ B @ A )
       != ( c_HOL_Otimes__class_Otimes @ C @ C @ A ) )
      | ( B
        = ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(348,axiom,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_1) ).

thf(1457,plain,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).

thf(517,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_1) ).

thf(1819,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(425,axiom,
    ! [A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__1__iff_0) ).

thf(1624,plain,
    ! [A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).

thf(3,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(682,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).

thf(327,axiom,
    class_Power_Opower @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Power_Opower) ).

thf(1407,plain,
    class_Power_Opower @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).

thf(430,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(1634,plain,
    class_Ring__and__Field_Oring__no__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(320,axiom,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__0__iff_0) ).

thf(1392,plain,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).

thf(564,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = B )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__nonneg_0) ).

thf(1910,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = B )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
       != ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).

thf(842,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
       != ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(325,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(1402,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)],[325]) ).

thf(576,axiom,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__1__iff_1) ).

thf(1936,plain,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(412,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I3_J_0) ).

thf(1592,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(18,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

thf(697,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).

thf(653,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(2100,plain,
    class_Ring__and__Field_Ono__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(290,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__self__iff_1) ).

thf(1328,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(166,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(1064,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)],[166]) ).

thf(537,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 @ C @ A ) @ ( c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ononneg__bounded_1) ).

thf(1856,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 @ C @ A ) @ ( c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(388,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(1540,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)],[388]) ).

thf(549,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(1878,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)],[549]) ).

thf(89,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
        = B )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__inverse__eq_0) ).

thf(869,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
        = B )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(187,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(1118,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)],[187]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) @ A )
        = ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__power__minus_0) ).

thf(989,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) @ A )
        = ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(323,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(1397,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)],[323]) ).

thf(91,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(874,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)],[91]) ).

thf(200,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ononneg__bounded_0) ).

thf(1143,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).

thf(534,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(1851,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)],[534]) ).

thf(494,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Omul__1_0) ).

thf(1772,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(254,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(1259,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)],[254]) ).

thf(385,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_Power_Opower__class_Opower @ B @ D @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inject__exp_0) ).

thf(1534,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( ( c_Power_Opower__class_Opower @ B @ C @ A )
       != ( c_Power_Opower__class_Opower @ B @ D @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(504,axiom,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__ge__one_0) ).

thf(1794,plain,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(184,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(1111,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)],[184]) ).

thf(239,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_1) ).

thf(1227,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(134,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__minus_0) ).

thf(980,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(410,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(1587,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)],[410]) ).

thf(197,axiom,
    ! [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_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_1) ).

thf(1138,plain,
    ! [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_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(470,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_0) ).

thf(1719,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).

thf(401,axiom,
    class_RealVector_Oreal__algebra__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1) ).

thf(1567,plain,
    class_RealVector_Oreal__algebra__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(96,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
        = ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__abs__inverse_0) ).

thf(884,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
        = ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).

thf(305,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(1361,plain,
    class_Ring__and__Field_Ono__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(219,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_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__mult__distrib_0) ).

thf(1182,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_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).

thf(479,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_RealVector_Oof__real @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__minus_0) ).

thf(1739,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_RealVector_Oof__real @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(409,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(1584,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)],[409]) ).

thf(461,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(1700,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)],[461]) ).

thf(512,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult_0) ).

thf(1810,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).

thf(554,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(1889,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)],[554]) ).

thf(27,axiom,
    class_Ring__and__Field_Omult__zero @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

thf(706,plain,
    class_Ring__and__Field_Omult__zero @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(332,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(1419,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)],[332]) ).

thf(152,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).

thf(1028,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).

thf(617,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_NthRoot_Osqrt @ A ) @ ( c_NthRoot_Osqrt @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_1) ).

thf(2023,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_NthRoot_Osqrt @ A ) @ ( c_NthRoot_Osqrt @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(579,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).

thf(1942,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).

thf(441,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(1659,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)],[441]) ).

thf(103,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__inverse__eq_0) ).

thf(901,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(7,axiom,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring__1) ).

thf(686,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(171,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(1075,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)],[171]) ).

thf(330,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(1414,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)],[330]) ).

thf(529,axiom,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ 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_real__sqrt__ge__zero_0) ).

thf(1842,plain,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ 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)],[529]) ).

thf(658,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(2108,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)],[658]) ).

thf(626,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(2038,plain,
    class_Ring__and__Field_Oordered__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).

thf(343,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Transcendental_Ocos @ A ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__le__one_0) ).

thf(1446,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Transcendental_Ocos @ A ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__imp__le__neg_0) ).

thf(1207,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(648,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__inverse_0) ).

thf(2085,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(420,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(1612,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)],[420]) ).

thf(1,negated_conjecture,
    ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ v_t____ @ ( c_RealVector_Onorm__class_Onorm @ v_w____ @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ v_w____ @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(679,plain,
    ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ v_t____ @ ( c_RealVector_Onorm__class_Onorm @ v_w____ @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_RealVector_Onorm__class_Onorm @ v_w____ @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(77,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(837,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)],[77]) ).

thf(520,axiom,
    class_Orderings_Olinorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).

thf(1825,plain,
    class_Orderings_Olinorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(668,axiom,
    class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add) ).

thf(2125,plain,
    class_OrderedGroup_Omonoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).

thf(22,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

thf(701,plain,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).

thf(274,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(1297,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)],[274]) ).

thf(387,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(1539,plain,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(259,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(1266,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)],[259]) ).

thf(194,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__minus_0) ).

thf(1131,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring__1 @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_Power_Opower__class_Opower @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ C @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).

thf(595,axiom,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ 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_real__sqrt__ge__0__iff_1) ).

thf(1974,plain,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ 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)],[595]) ).

thf(393,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Complex_ORe @ A ) @ ( c_RealVector_Onorm__class_Onorm @ A @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_complex__Re__le__cmod_0) ).

thf(1552,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Complex_ORe @ A ) @ ( c_RealVector_Onorm__class_Onorm @ A @ tc_Complex_Ocomplex ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(161,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ B @ A )
       != ( c_RealVector_Oof__real @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__eq__iff_0) ).

thf(1050,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ B @ A )
       != ( c_RealVector_Oof__real @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).

thf(507,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(1799,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)],[507]) ).

thf(546,axiom,
    class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector) ).

thf(1874,plain,
    class_RealVector_Oreal__normed__vector @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(336,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(1429,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)],[336]) ).

thf(468,axiom,
    ! [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_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_0) ).

thf(1715,plain,
    ! [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_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(256,axiom,
    class_Ring__and__Field_Olordered__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring) ).

thf(1263,plain,
    class_Ring__and__Field_Olordered__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(140,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(997,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)],[140]) ).

thf(204,axiom,
    class_OrderedGroup_Oab__group__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).

thf(1150,plain,
    class_OrderedGroup_Oab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).

thf(359,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(1478,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)],[359]) ).

thf(250,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Oneg__mul_0) ).

thf(1249,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).

thf(224,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Opos__bounded_0) ).

thf(1192,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__left__Xpos__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(574,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(1932,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)],[574]) ).

thf(610,axiom,
    ( ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal )
   != ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__zero__not__eq__one_0) ).

thf(2006,plain,
    ( ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal )
   != ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(34,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(721,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)],[34]) ).

thf(633,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ 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_abs__eq__mult_0) ).

thf(2052,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ 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)],[633]) ).

thf(415,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__one_0) ).

thf(1599,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).

thf(248,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Opos__bounded_0) ).

thf(1246,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__right__Xpos__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(292,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(1333,plain,
    class_Ring__and__Field_Ocomm__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(285,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(1318,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)],[285]) ).

thf(228,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(1202,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)],[228]) ).

thf(497,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 @ C @ A ) @ ( c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Obounded_0) ).

thf(1779,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 @ C @ A ) @ ( c_RealVector_Osko__RealVector__Xmult__right__Xbounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(111,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(921,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)],[111]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__imp__less__neg_0) ).

thf(1035,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

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 ) @ ( 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(1187,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)],[221]) ).

thf(151,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).

thf(1026,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).

thf(61,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add__distrib_0) ).

thf(794,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).

thf(476,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_0) ).

thf(1732,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(514,axiom,
    class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring) ).

thf(1814,plain,
    class_Ring__and__Field_Odivision__ring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).

thf(117,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
       != B )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_0) ).

thf(938,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
       != B )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).

thf(636,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(2057,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)],[636]) ).

thf(467,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(1712,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)],[467]) ).

thf(531,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(1846,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)],[531]) ).

thf(123,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__imp__negative_0) ).

thf(953,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).

thf(220,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__one_0) ).

thf(1185,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).

thf(33,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(718,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)],[33]) ).

thf(98,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(888,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)],[98]) ).

thf(264,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(1278,plain,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).

thf(437,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(1648,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)],[437]) ).

thf(474,axiom,
    ! [A: $i] :
      ( ( ( c_Transcendental_Ocos @ A )
       != ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Osin @ A )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__one__sin__zero_0) ).

thf(1727,plain,
    ! [A: $i] :
      ( ( ( c_Transcendental_Ocos @ A )
       != ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Osin @ A )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).

thf(490,axiom,
    class_OrderedGroup_Olordered__ab__group__add__abs @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs) ).

thf(1764,plain,
    class_OrderedGroup_Olordered__ab__group__add__abs @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).

thf(202,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_NthRoot_Osqrt @ A ) @ ( c_NthRoot_Osqrt @ B ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_0) ).

thf(1146,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_NthRoot_Osqrt @ A ) @ ( c_NthRoot_Osqrt @ B ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(623,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__leI_0) ).

thf(2033,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(72,axiom,
    ! [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_Oinverse @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_1) ).

thf(824,plain,
    ! [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_Oinverse @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).

thf(482,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__le__iff__le_0) ).

thf(1747,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(391,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(1548,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)],[391]) ).

thf(10,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

thf(689,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(38,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(733,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)],[38]) ).

thf(666,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(2121,plain,
    class_Ring__and__Field_Ozero__neq__one @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).

thf(678,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(2144,plain,
    class_Ring__and__Field_Oordered__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).

thf(460,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(1698,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)],[460]) ).

thf(181,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_0) ).

thf(1103,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).

thf(620,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(2028,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)],[620]) ).

thf(413,axiom,
    ! [A: $i] :
      ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__1_0) ).

thf(1595,plain,
    ! [A: $i] :
      ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(206,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(1154,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)],[206]) ).

thf(70,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).

thf(819,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).

thf(318,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(1389,plain,
    class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(191,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__eq__nonneg_1) ).

thf(1125,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(53,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(772,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)],[53]) ).

thf(42,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__abs_0) ).

thf(743,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).

thf(73,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__unique_0) ).

thf(826,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).

thf(590,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult) ).

thf(1965,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).

thf(104,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(904,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)],[104]) ).

thf(132,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(975,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)],[132]) ).

thf(144,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(1007,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)],[144]) ).

thf(15,axiom,
    class_Ring__and__Field_Ocomm__semiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

thf(694,plain,
    class_Ring__and__Field_Ocomm__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(253,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__inverse__mult__distrib_0) ).

thf(1256,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(364,axiom,
    class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra) ).

thf(1488,plain,
    class_RealVector_Oreal__normed__algebra @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).

thf(464,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(1707,plain,
    class_OrderedGroup_Olordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(261,axiom,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_t____ @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_t_I1_J_0) ).

thf(1271,plain,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ v_t____ @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(281,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(1312,plain,
    class_Ring__and__Field_Oordered__ring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(542,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(1865,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)],[542]) ).

thf(431,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_1) ).

thf(1635,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(164,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oabs__if @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = B )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if_1) ).

thf(1058,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oabs__if @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = B )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(25,axiom,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

thf(704,plain,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ominus_0) ).

thf(1464,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(245,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(1239,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)],[245]) ).

thf(605,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__gt__1__iff_0) ).

thf(1997,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(634,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(2055,plain,
    class_Ring__and__Field_Oring__1__no__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(177,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(1092,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)],[177]) ).

thf(491,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(1765,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)],[491]) ).

thf(176,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(1090,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)],[176]) ).

thf(110,axiom,
    ! [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_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_2) ).

thf(919,plain,
    ! [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_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(65,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(804,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)],[65]) ).

thf(433,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(1638,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)],[433]) ).

thf(238,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(1224,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)],[238]) ).

thf(50,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(764,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)],[50]) ).

thf(225,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(1194,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)],[225]) ).

thf(645,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(2079,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)],[645]) ).

thf(267,axiom,
    ! [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_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_1) ).

thf(1282,plain,
    ! [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_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(647,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(2084,plain,
    class_Ring__and__Field_Omult__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(57,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(784,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)],[57]) ).

thf(381,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(1524,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)],[381]) ).

thf(160,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(1048,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)],[160]) ).

thf(652,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(2097,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)],[652]) ).

thf(367,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ 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_abs__eq__mult_2) ).

thf(1492,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ 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)],[367]) ).

thf(471,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(1722,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)],[471]) ).

thf(663,axiom,
    class_Ring__and__Field_Oring__1 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring__1) ).

thf(2116,plain,
    class_Ring__and__Field_Oring__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).

thf(40,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(737,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)],[40]) ).

thf(189,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(1122,plain,
    class_Ring__and__Field_Opordered__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).

thf(456,axiom,
    class_OrderedGroup_Ogroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).

thf(1690,plain,
    class_OrderedGroup_Ogroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).

thf(313,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(1376,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)],[313]) ).

thf(87,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonzero__iff__nonzero_1) ).

thf(863,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).

thf(232,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__one_0) ).

thf(1209,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_Power_Opower__class_Opower @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).

thf(665,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__zero__iff_1) ).

thf(2119,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).

thf(2,axiom,
    class_Ring__and__Field_Opordered__semiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).

thf(681,plain,
    class_Ring__and__Field_Opordered__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(535,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(1853,plain,
    class_Ring__and__Field_Omult__zero @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).

thf(328,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(1408,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)],[328]) ).

thf(94,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(880,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)],[94]) ).

thf(158,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(1043,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)],[158]) ).

thf(592,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_NthRoot_Osqrt @ A ) @ ( c_NthRoot_Osqrt @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__less__iff_1) ).

thf(1969,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_NthRoot_Osqrt @ A ) @ ( c_NthRoot_Osqrt @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(279,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ 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_real__sqrt__gt__zero_0) ).

thf(1307,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ 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)],[279]) ).

thf(445,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_RealVector_Oof__real @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Ominus_0) ).

thf(1667,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_RealVector_Oof__real @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(355,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(1471,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)],[355]) ).

thf(618,axiom,
    class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oidom) ).

thf(2025,plain,
    class_Ring__and__Field_Oidom @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(48,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(758,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)],[48]) ).

thf(670,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(2129,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)],[670]) ).

thf(69,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(816,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)],[69]) ).

thf(518,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(1821,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)],[518]) ).

thf(210,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_RealDef_Oreal ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_RealVector_Oof__real @ B @ A ) @ ( c_RealVector_Oof__real @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__mult_0) ).

thf(1162,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_RealDef_Oreal ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_RealVector_Oof__real @ B @ A ) @ ( c_RealVector_Oof__real @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(540,axiom,
    class_Ring__and__Field_Oring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).

thf(1862,plain,
    class_Ring__and__Field_Oring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(289,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__eq__0__iff_0) ).

thf(1325,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(108,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).

thf(915,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(297,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(1344,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)],[297]) ).

thf(119,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__0__iff__equal_0) ).

thf(943,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).

thf(272,axiom,
    class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add) ).

thf(1293,plain,
    class_OrderedGroup_Oab__group__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).

thf(315,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(1381,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)],[315]) ).

thf(85,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(858,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)],[85]) ).

thf(396,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(1557,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)],[396]) ).

thf(81,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).

thf(848,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).

thf(21,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(700,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(115,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(932,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)],[115]) ).

thf(165,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = B )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__if__lattice_1) ).

thf(1061,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = B )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).

thf(584,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(1952,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)],[584]) ).

thf(528,axiom,
    class_Ring__and__Field_Oabs__if @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if) ).

thf(1841,plain,
    class_Ring__and__Field_Oabs__if @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

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

thf(1474,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).

thf(125,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(959,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)],[125]) ).

thf(16,axiom,
    class_Ring__and__Field_Omult__mono @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).

thf(695,plain,
    class_Ring__and__Field_Omult__mono @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).

thf(435,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
       != ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__1__iff_0) ).

thf(1643,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
       != ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).

thf(675,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(2139,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)],[675]) ).

thf(216,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(1176,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)],[216]) ).

thf(136,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(986,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)],[136]) ).

thf(185,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__le__inverse__iff_2) ).

thf(1113,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).

thf(654,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__gt1__lemma_0) ).

thf(2101,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).

thf(458,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(1694,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)],[458]) ).

thf(641,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(2069,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)],[641]) ).

thf(399,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__Suc__less_0) ).

thf(1562,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(107,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(912,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)],[107]) ).

thf(6,axiom,
    class_Orderings_Opreorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(685,plain,
    class_Orderings_Opreorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).

thf(213,axiom,
    class_Ring__and__Field_Osemiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).

thf(1171,plain,
    class_Ring__and__Field_Osemiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(135,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__neg_0) ).

thf(983,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ B @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).

thf(643,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).

thf(2075,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(167,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(1066,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)],[167]) ).

thf(342,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(1445,plain,
    class_Ring__and__Field_Omult__mono1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(639,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ 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_abs__eq__mult_1) ).

thf(2064,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ 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)],[639]) ).

thf(147,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__zero__imp__zero_0) ).

thf(1015,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(495,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__neg_0) ).

thf(1775,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).

thf(338,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__right_0) ).

thf(1435,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(473,axiom,
    class_Int_Onumber__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).

thf(1726,plain,
    class_Int_Onumber__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(307,axiom,
    class_RealVector_Oreal__algebra__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1) ).

thf(1364,plain,
    class_RealVector_Oreal__algebra__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).

thf(594,axiom,
    class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Ofield) ).

thf(1973,plain,
    class_Ring__and__Field_Ofield @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(509,axiom,
    ! [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_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_2) ).

thf(1805,plain,
    ! [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_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(426,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(1626,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)],[426]) ).

thf(582,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__neg__nonpos_1) ).

thf(1948,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(487,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(1758,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)],[487]) ).

thf(353,axiom,
    ! [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_Oinverse @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_1) ).

thf(1467,plain,
    ! [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_Oinverse @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(562,axiom,
    ! [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_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonnegative__iff__nonnegative_0) ).

thf(1905,plain,
    ! [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_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).

thf(113,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 @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_0) ).

thf(927,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 @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(453,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add) ).

thf(1684,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(195,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(1134,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)],[195]) ).

thf(602,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(1990,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)],[602]) ).

thf(587,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(1958,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)],[587]) ).

thf(46,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(754,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)],[46]) ).

thf(129,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(968,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)],[129]) ).

thf(277,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(1304,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)],[277]) ).

thf(545,axiom,
    class_Ring__and__Field_Ofield @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).

thf(1873,plain,
    class_Ring__and__Field_Ofield @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(173,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(1081,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)],[173]) ).

thf(44,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
        = ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__inverse_0) ).

thf(749,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
        = ( c_Power_Opower__class_Opower @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).

thf(201,axiom,
    class_Ring__and__Field_Oidom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).

thf(1145,plain,
    class_Ring__and__Field_Oidom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).

thf(148,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(1018,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)],[148]) ).

thf(506,axiom,
    class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

thf(1798,plain,
    class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(31,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__zero_0) ).

thf(712,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).

thf(84,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
       != ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).

thf(855,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
       != ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).

thf(97,axiom,
    class_Ring__and__Field_Omult__mono1 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).

thf(887,plain,
    class_Ring__and__Field_Omult__mono1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(130,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__imp__inverse__less_0) ).

thf(971,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).

thf(251,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__D2_0) ).

thf(1252,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).

thf(310,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oabs__class_Oabs @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_estimate__by__abs_0) ).

thf(1368,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add__abs @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Oabs__class_Oabs @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).

thf(485,axiom,
    ! [A: $i] :
      ( ( ( c_NthRoot_Osqrt @ A )
       != ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__1__iff_0) ).

thf(1753,plain,
    ! [A: $i] :
      ( ( ( c_NthRoot_Osqrt @ A )
       != ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(179,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = B )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__of__pos_0) ).

thf(1098,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ B @ A )
        = B )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).

thf(11,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(690,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).

thf(377,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__one_0) ).

thf(1516,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(169,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
        = ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__idempotent_0) ).

thf(1070,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
        = ( c_HOL_Oabs__class_Oabs @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(90,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(872,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)],[90]) ).

thf(26,axiom,
    class_Ring__and__Field_Oordered__semiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

thf(705,plain,
    class_Ring__and__Field_Oordered__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).

thf(207,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(1156,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)],[207]) ).

thf(637,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(2060,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)],[637]) ).

thf(324,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(1400,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).

thf(28,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

thf(707,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).

thf(240,axiom,
    ! [B: $i,A: $i] :
      ( ( c_NthRoot_Osqrt @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Otimes__class_Otimes @ ( c_NthRoot_Osqrt @ A ) @ ( c_NthRoot_Osqrt @ B ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__mult_0) ).

thf(1230,plain,
    ! [B: $i,A: $i] :
      ( ( c_NthRoot_Osqrt @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Otimes__class_Otimes @ ( c_NthRoot_Osqrt @ A ) @ ( c_NthRoot_Osqrt @ B ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).

thf(362,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__less_0) ).

thf(1484,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).

thf(162,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(1053,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)],[162]) ).

thf(337,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(1432,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)],[337]) ).

thf(60,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(791,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)],[60]) ).

thf(243,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( 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_neg__le__0__iff__le_1) ).

thf(1235,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( 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)],[243]) ).

thf(122,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ 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_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__less__iff__less_0) ).

thf(951,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ 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_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).

thf(451,axiom,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__zero_0) ).

thf(1679,plain,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(629,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(2044,plain,
    class_OrderedGroup_Opordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).

thf(269,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(1285,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)],[269]) ).

thf(236,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__minus_0) ).

thf(1220,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(105,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(907,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)],[105]) ).

thf(513,axiom,
    class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1) ).

thf(1813,plain,
    class_RealVector_Oreal__normed__algebra__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).

thf(275,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(1300,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)],[275]) ).

thf(432,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(1637,plain,
    class_Ring__and__Field_Omult__mono @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(78,axiom,
    ! [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_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__negative__iff__negative_0) ).

thf(840,plain,
    ! [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_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(500,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(1785,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)],[500]) ).

thf(284,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__semigroup__add) ).

thf(1317,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).

thf(523,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(1830,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)],[523]) ).

thf(489,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(1763,plain,
    class_Ring__and__Field_Ocomm__semiring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(635,axiom,
    class_OrderedGroup_Oordered__ab__group__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add) ).

thf(2056,plain,
    class_OrderedGroup_Oordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(575,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(1934,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)],[575]) ).

thf(389,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal )
       != ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squares__cancel__a_0) ).

thf(1543,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal )
       != ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(558,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(1898,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)],[558]) ).

thf(268,axiom,
    class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1) ).

thf(1284,plain,
    class_Ring__and__Field_Oring__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(373,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(1506,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)],[373]) ).

thf(483,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(1749,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)],[483]) ).

thf(446,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).

thf(1670,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(262,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__1__left_0) ).

thf(1272,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Omonoid__mult @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).

thf(92,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(876,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)],[92]) ).

thf(422,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_Osko__RealVector__Xmult__left__Xbounded__1__1 @ C @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Obounded_0) ).

thf(1617,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_Osko__RealVector__Xmult__left__Xbounded__1__1 @ C @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(661,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add) ).

thf(2113,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).

thf(24,axiom,
    class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ono__zero__divisors) ).

thf(703,plain,
    class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_1) ).

thf(1141,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(598,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_Transcendental_Osin @ A ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__le__one_0) ).

thf(1981,plain,
    ! [A: $i] : ( c_lessequals @ ( c_Transcendental_Osin @ A ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(508,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(1802,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)],[508]) ).

thf(150,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(1023,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)],[150]) ).

thf(301,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(1353,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)],[301]) ).

thf(586,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(1955,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)],[586]) ).

thf(372,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__0__iff_0) ).

thf(1504,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).

thf(36,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(727,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)],[36]) ).

thf(133,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( 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_neg__less__0__iff__less_1) ).

thf(978,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( 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)],[133]) ).

thf(198,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__mult) ).

thf(1140,plain,
    class_OrderedGroup_Omonoid__mult @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).

thf(469,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ononneg__bounded_0) ).

thf(1717,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__Xnonneg__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(621,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(2030,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)],[621]) ).

thf(80,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__minus_0) ).

thf(845,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).

thf(333,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(1421,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)],[333]) ).

thf(527,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_NthRoot_Osqrt @ A ) @ ( c_NthRoot_Osqrt @ B ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__le__iff_0) ).

thf(1839,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_NthRoot_Osqrt @ A ) @ ( c_NthRoot_Osqrt @ B ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(174,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__abs__iff_1) ).

thf(1084,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).

thf(649,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__left_0) ).

thf(2088,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(218,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(1180,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)],[218]) ).

thf(591,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(1966,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)],[591]) ).

thf(454,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__self__iff_0) ).

thf(1685,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Olordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(394,axiom,
    class_Ring__and__Field_Odivision__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring) ).

thf(1553,plain,
    class_Ring__and__Field_Odivision__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(516,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(1817,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)],[516]) ).

thf(439,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(1654,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)],[439]) ).

thf(222,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__right_Ononneg__bounded_0) ).

thf(1189,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealVector_Osko__RealVector__Xmult__right__Xnonneg__bounded__1__1 @ B @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).

thf(346,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).

thf(1453,plain,
    class_OrderedGroup_Omonoid__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(183,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__equal__zero_1) ).

thf(1108,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Oordered__ab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(349,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(1459,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)],[349]) ).

thf(630,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(2045,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)],[630]) ).

thf(287,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(1321,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)],[287]) ).

thf(525,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 @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__power__abs_0) ).

thf(1834,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 @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(565,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(1913,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)],[565]) ).

thf(530,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(1844,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)],[530]) ).

thf(9,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

thf(688,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).

thf(498,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_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 @ C @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__left_Ononneg__bounded_1) ).

thf(1781,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_Osko__RealVector__Xmult__left__Xnonneg__bounded__1__1 @ C @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(99,axiom,
    ! [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_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__less__inverse__iff_0) ).

thf(891,plain,
    ! [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_Oone__class_Oone @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(659,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(2110,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)],[659]) ).

thf(319,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(1390,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)],[319]) ).

thf(477,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(1734,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)],[477]) ).

thf(510,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(1807,plain,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(411,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).

thf(1590,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(436,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(1646,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)],[436]) ).

thf(20,axiom,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add) ).

thf(699,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).

thf(127,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__neg__iff__add__eq__0_0) ).

thf(963,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(448,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(1674,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)],[448]) ).

thf(673,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).

thf(2135,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(374,axiom,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ A )
      | ( ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_norm__one_0) ).

thf(1508,plain,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra__1 @ A )
      | ( ( c_RealVector_Onorm__class_Onorm @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(481,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(1745,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)],[481]) ).

thf(619,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_1) ).

thf(2026,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(536,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(1854,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)],[536]) ).

thf(247,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(1244,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)],[247]) ).

thf(58,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 )
      | ( B
        = ( c_HOL_Ouminus__class_Ouminus @ D @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__cancel__end_0) ).

thf(786,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 )
      | ( B
        = ( c_HOL_Ouminus__class_Ouminus @ D @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).

thf(56,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__0__equal__iff__equal_1) ).

thf(781,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).

thf(126,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__not__less__zero_0) ).

thf(961,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(68,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).

thf(813,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Lattices_Oboolean__algebra @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).

thf(296,axiom,
    ! [A: $i] :
      ( ( ( c_NthRoot_Osqrt @ A )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__eq__zero__cancel_0) ).

thf(1341,plain,
    ! [A: $i] :
      ( ( ( c_NthRoot_Osqrt @ A )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).

thf(101,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(896,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)],[101]) ).

thf(120,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
       != ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__eq__iff__eq_0) ).

thf(946,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ B @ A )
       != ( c_HOL_Oinverse__class_Oinverse @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(180,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_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__less__iff_0) ).

thf(1101,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_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).

thf(428,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(1629,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)],[428]) ).

thf(609,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(2004,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)],[609]) ).

thf(611,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(2009,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)],[611]) ).

thf(153,axiom,
    ! [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_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__positive__iff__positive_0) ).

thf(1030,plain,
    ! [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_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(646,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__semiring_Osemiring__rules_I12_J_0) ).

thf(2081,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ocomm__semiring__1 @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(628,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__minus_0) ).

thf(2041,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(496,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).

thf(1777,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).

thf(273,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Ominus__right_0) ).

thf(1294,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).

thf(233,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(1212,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)],[233]) ).

thf(418,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(1607,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(376,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(1513,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)],[376]) ).

thf(442,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(1661,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)],[442]) ).

thf(615,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(2019,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)],[615]) ).

thf(159,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(1045,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)],[159]) ).

thf(340,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse_0) ).

thf(1440,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).

thf(114,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(929,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)],[114]) ).

thf(75,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__self__iff_1) ).

thf(832,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).

thf(5,axiom,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__cancel__semiring) ).

thf(684,plain,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).

thf(556,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(1893,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)],[556]) ).

thf(625,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(2036,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)],[625]) ).

thf(280,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(1309,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)],[280]) ).

thf(421,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ( ( c_HOL_Oone__class_Oone @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__neq__zero_0) ).

thf(1614,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ozero__neq__one @ A )
      | ( ( c_HOL_Oone__class_Oone @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(63,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(800,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)],[63]) ).

thf(299,axiom,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real__1_0) ).

thf(1348,plain,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).

thf(141,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(999,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)],[141]) ).

thf(45,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(752,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)],[45]) ).

thf(450,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(1678,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(390,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(1546,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)],[390]) ).

thf(322,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(1395,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)],[322]) ).

thf(548,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(1876,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)],[548]) ).

thf(203,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(1148,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)],[203]) ).

thf(249,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(1248,plain,
    class_Ring__and__Field_Oring__no__zero__divisors @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(360,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__one__less__zero_0) ).

thf(1480,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).

thf(39,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(735,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)],[39]) ).

thf(608,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(2003,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).

thf(677,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Ocos @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__minus_0) ).

thf(2142,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Ocos @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(368,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__inverse__le__neg_0) ).

thf(1495,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(66,axiom,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__eq__0_1) ).

thf(807,plain,
    ! [A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(294,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_square__eq__iff_1) ).

thf(1335,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).

thf(398,axiom,
    class_Orderings_Opreorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).

thf(1561,plain,
    class_Orderings_Opreorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(214,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__le__zero_0) ).

thf(1172,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).

thf(650,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(2091,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)],[650]) ).

thf(555,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(1891,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)],[555]) ).

thf(356,axiom,
    class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring) ).

thf(1473,plain,
    class_Ring__and__Field_Osemiring @ tc_Complex_Ocomplex,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).

thf(17,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le) ).

thf(696,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(211,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(1165,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)],[211]) ).

thf(480,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(1742,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)],[480]) ).

thf(163,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(1056,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)],[163]) ).

thf(502,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(1789,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)],[502]) ).

thf(270,axiom,
    ! [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_Oone__class_Oone @ A ) @ B @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__less__1__iff_0) ).

thf(1288,plain,
    ! [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_Oone__class_Oone @ A ) @ B @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(466,axiom,
    ! [A: $i] :
      ( ( c_NthRoot_Osqrt @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__minus_0) ).

thf(1710,plain,
    ! [A: $i] :
      ( ( c_NthRoot_Osqrt @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_NthRoot_Osqrt @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).

thf(616,axiom,
    ! [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_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__nonpositive__iff__nonpositive_0) ).

thf(2021,plain,
    ! [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_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

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 @ 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(1346,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)],[298]) ).

thf(573,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ 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_real__sqrt__gt__0__iff_1) ).

thf(1930,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ 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)],[573]) ).

thf(41,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
        = ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__abs_0) ).

thf(740,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A )
        = ( c_Power_Opower__class_Opower @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).

thf(193,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(1129,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)],[193]) ).

thf(255,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(1261,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)],[255]) ).

thf(408,axiom,
    ( ( c_NthRoot_Osqrt @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__one_0) ).

thf(1582,plain,
    ( ( c_NthRoot_Osqrt @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(303,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(1357,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)],[303]) ).

thf(138,axiom,
    ! [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_Oinverse @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_positive__imp__inverse__positive_0) ).

thf(992,plain,
    ! [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_Oinverse @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).

thf(571,axiom,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__real_Ozero_0) ).

thf(1925,plain,
    ! [A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__vector @ A )
      | ~ ( class_RealVector_Oreal__algebra__1 @ A )
      | ( ( c_RealVector_Oof__real @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(82,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(850,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)],[82]) ).

thf(552,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(1885,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)],[552]) ).

thf(424,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(1621,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)],[424]) ).

thf(188,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(1120,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)],[188]) ).

thf(384,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_0) ).

thf(1532,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).

thf(86,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(860,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)],[86]) ).

thf(316,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__mult__commute_0) ).

thf(1384,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(386,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_power__less__power__Suc_0) ).

thf(1537,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__semidom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Power_Opower__class_Opower @ B @ C @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(596,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(1976,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)],[596]) ).

thf(392,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(1550,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)],[392]) ).

thf(370,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(1500,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)],[370]) ).

thf(570,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(1923,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)],[570]) ).

thf(414,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(1597,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)],[414]) ).

thf(550,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(1880,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)],[550]) ).

thf(143,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__minus__eq_0) ).

thf(1004,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).

thf(560,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__0__iff__le_0) ).

thf(1902,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).

thf(12,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(691,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(286,axiom,
    class_Power_Opower @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Power_Opower) ).

thf(1320,plain,
    class_Power_Opower @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).

thf(589,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__1_0) ).

thf(1962,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Odivision__ring @ A )
      | ( ( c_HOL_Oinverse__class_Oinverse @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(452,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__mult__self_0) ).

thf(1681,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ A )
        = ( c_HOL_Otimes__class_Otimes @ B @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(351,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(1463,plain,
    class_Ring__and__Field_Odivision__by__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(532,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(1848,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)],[532]) ).

thf(229,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(1204,plain,
    class_Ring__and__Field_Opordered__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(657,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(2106,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)],[657]) ).

thf(29,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

thf(708,plain,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).

thf(95,axiom,
    ! [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_Oinverse @ 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_inverse__negative__iff__negative_1) ).

thf(882,plain,
    ! [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_Oinverse @ 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)],[95]) ).

thf(331,axiom,
    ! [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_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inverse__le__1__iff_1) ).

thf(1417,plain,
    ! [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_Oinverse @ B @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).

thf(116,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(935,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)],[116]) ).

thf(581,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(1945,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)],[581]) ).

thf(145,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(1009,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)],[145]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__inverse__le_0) ).

thf(1490,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Oinverse @ B @ A ) @ ( c_HOL_Oinverse__class_Oinverse @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(156,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__add_0) ).

thf(1037,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).

thf(54,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(775,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)],[54]) ).

thf(493,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(1769,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)],[493]) ).

thf(567,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__lt__1__iff_0) ).

thf(1917,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_NthRoot_Osqrt @ A ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(12758,plain,
    $false,
    inference(e,[status(thm)],[1665,1469,1823,1995,1237,909,893,1982,941,1950,1554,2094,1411,2131,1454,2072,1767,1559,1105,1315,1850,2077,1158,2117,683,1068,1522,2062,994,1939,1073,2014,1205,1971,1486,730,1290,1443,1808,2114,1269,1671,1756,2035,715,1233,698,1761,1954,1222,1497,1705,1078,1788,1426,1999,797,1275,2141,1919,1988,1196,898,1001,1127,1576,709,973,1921,1359,1366,1887,829,1095,1724,1475,2067,1529,1904,1518,1265,1703,1482,1254,1628,724,1792,1985,2039,1871,1907,1323,802,1826,1577,1992,2126,1462,949,1330,1860,1264,1511,917,702,1313,1279,1832,1191,1379,1087,2049,1609,770,1115,1568,1641,1815,1362,1875,1232,1489,924,789,1373,1334,1151,1960,966,821,2017,1302,756,1664,2105,1450,1040,1632,1136,834,1858,2122,1828,1978,766,1928,1215,866,1796,1394,1351,1943,1242,1521,1696,1564,1169,687,1896,692,1447,956,1526,2137,2103,1405,1863,1651,1604,2011,1691,1438,1306,1199,761,810,1338,2047,1783,1736,1868,2000,1730,1915,1708,746,1123,1217,693,2032,1883,1387,1900,1021,778,1355,1580,1570,1174,1676,2133,1502,1751,1619,1370,1423,1938,1365,879,852,1178,1159,1836,1656,1281,2112,1573,1012,1032,1602,1687,1457,1819,1624,682,1407,1634,1392,1910,842,1402,1936,1592,697,2100,1328,1064,1856,1540,1878,869,1118,989,1397,874,1143,1851,1772,1259,1534,1794,1111,1227,980,1587,1138,1719,1567,884,1361,1182,1739,1584,1700,1810,1889,706,1419,1028,2023,1942,1659,901,686,1075,1414,1842,2108,2038,1446,1207,2085,1612,679,837,1825,2125,701,1297,1539,1266,1131,1974,1552,1050,1799,1874,1429,1715,1263,997,1150,1478,1249,1192,1932,2006,721,2052,1599,1246,1333,1318,1202,1779,921,1035,1187,1026,794,1732,1814,938,2057,1712,1846,953,1185,718,888,1278,1648,1727,1764,1146,2033,824,1747,1548,689,733,2121,2144,1698,1103,2028,1595,1154,819,1389,1125,772,743,826,1965,904,975,1007,694,1256,1488,1707,1271,1312,1865,1635,1058,704,1464,1239,1997,2055,1092,1765,1090,919,804,1638,1224,764,1194,2079,1282,2084,784,1524,1048,2097,1492,1722,2116,737,1122,1690,1376,863,1209,2119,681,1853,1408,880,1043,1969,1307,1667,1471,2025,758,2129,816,1821,1162,1862,1325,915,1344,943,1293,1381,858,1557,848,700,932,1061,1952,1841,1474,959,695,1643,2139,1176,986,1113,2101,1694,2069,1562,912,685,1171,983,2075,1066,1445,2064,1015,1775,1435,1726,1364,1973,1805,1626,1948,1758,1467,1905,927,1684,1134,1990,1958,754,968,1304,1873,1081,749,1145,1018,1798,712,855,887,971,1252,1368,1753,1098,690,1516,1070,872,705,1156,2060,1400,707,1230,1484,1053,1432,791,1235,951,1679,2044,1285,1220,907,1813,1300,1637,840,1785,1317,1830,1763,2056,1934,1543,1898,1284,1506,1749,1670,1272,876,1617,2113,703,1141,1981,1802,1023,1353,1955,1504,727,978,1140,1717,2030,845,1421,1839,1084,2088,1180,1966,1685,1553,1817,1654,1189,1453,1108,1459,2045,1321,1834,1913,1844,688,1781,891,2110,1390,1734,1807,1590,1646,699,963,1674,2135,1508,1745,2026,1854,1244,786,781,961,813,1341,896,946,1101,1629,2004,2009,1030,2081,2041,1777,1294,1212,1607,1513,1661,2019,1045,1440,929,832,684,1893,2036,1309,1614,800,1348,999,752,1678,1546,1395,1876,1148,1248,1480,735,2003,2142,1495,807,1335,1561,1172,2091,1891,1473,696,1165,1742,1056,1789,1288,1710,2021,1346,1930,740,1129,1261,1582,1357,992,1925,850,1885,1621,1120,1532,860,1384,1537,1976,1550,1500,1923,1597,1880,1004,1902,691,1320,1962,1681,1463,1848,1204,2106,708,882,1417,935,1945,1009,1490,1037,775,1769,1917]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10  % Problem  : ALG406-1 : TPTP v8.2.0. Released v4.1.0.
% 0.09/0.12  % Command  : run_Leo-III %s %d
% 0.12/0.32  % Computer : n008.cluster.edu
% 0.12/0.32  % Model    : x86_64 x86_64
% 0.12/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32  % Memory   : 8042.1875MB
% 0.12/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32  % CPULimit : 300
% 0.12/0.32  % WCLimit  : 300
% 0.12/0.32  % DateTime : Sat May 18 22:39:24 EDT 2024
% 0.12/0.32  % CPUTime  : 
% 1.00/0.95  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.88/1.29  % [INFO] 	 Parsing done (331ms). 
% 1.88/1.30  % [INFO] 	 Running in sequential loop mode. 
% 2.73/1.66  % [INFO] 	 eprover registered as external prover. 
% 2.73/1.66  % [INFO] 	 cvc4 registered as external prover. 
% 2.73/1.67  % [INFO] 	 Scanning for conjecture ... 
% 3.29/1.84  % [INFO] 	 Found a conjecture (or negated_conjecture) and 677 axioms. Running axiom selection ... 
% 3.84/2.03  % [INFO] 	 Axiom selection finished. Selected 677 axioms (removed 0 axioms). 
% 4.90/2.29  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.90/2.32  % [INFO] 	 Type checking passed. 
% 4.90/2.32  % [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 ... 
% 60.63/12.37  % External prover 'e' found a proof!
% 60.63/12.37  % [INFO] 	 Killing All external provers ... 
% 60.98/12.37  % Time passed: 11900ms (effective reasoning time: 11068ms)
% 60.98/12.38  % Axioms used in derivation (677): cls_abs__le__zero__iff_0, cls_real__mult__is__one_1, clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add, cls_add__0__left_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_add__cancel__end_1, cls_add__pos__nonneg_0, cls_minus__le__iff_0, clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if, cls_neg__0__le__iff__le_1, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_not__one__less__zero_0, cls_mult__less__cancel__left__disj_5, cls_sin__le__one_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1, cls_mult__left_Ononneg__bounded_1, cls_order__le__less__trans_0, cls_mult__zero__right_0, cls_zero__less__one_0, cls_abs__if__lattice_0, cls_abs__le__iff_2, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_comm__semiring__class_Odistrib_0, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra, cls_mult__left_Obounded_0, cls_le__minus__self__iff_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_abs__of__nonneg_0, cls_real__mult__le__cancel__iff1_0, cls_real__mult__assoc_0, cls_mult__less__cancel__right__disj_0, cls_real__sqrt__zero_0, cls_mult__nonneg__nonpos2_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ofield, cls_square__eq__iff_1, cls_class__semiring_Osemiring__rules_I9_J_0, cls_real__mult__le__cancel__iff2_1, cls_minus__zero_0, cls_norm__zero_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__mult, cls_inverse__zero__imp__zero_0, cls_xt1_I12_J_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring__1__no__zero__divisors, cls_real__less__def_1, cls_sum__squares__eq__zero__iff_0, cls_zero__less__norm__iff_1, cls_negative__imp__inverse__negative_0, cls_left__minus_0, clsarity_RealDef__Oreal__RealVector_Oreal__algebra__1, cls_mult__less__cancel__left__disj_1, cls_zero__le__one_0, cls_add__increasing2_0, cls_inverse__eq__iff__eq_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring, cls_inverse__le__1__iff_2, cls_not__sum__squares__lt__zero_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_pos__add__strict_0, cls_abs__minus__le__zero_0, cls_power__inject__exp_0, cls_zero__le__mult__iff_3, cls_linorder__neqE_0, cls_real__sqrt__gt__0__iff_1, cls_add__strict__right__mono_0, cls_power__le__zero__eq_3, cls_class__semiring_Osemiring__rules_I21_J_0, cls_minus__add__distrib_0, cls_abs__eq__mult_1, clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add, cls_less__imp__inverse__less__neg_0, clsarity_nat__OrderedGroup_Omonoid__add, cls_add__imp__eq_0, cls_abs__mult__less_0, cls_compl__eq__compl__iff_0, cls_inverse__less__1__iff_2, cls_add__le__cancel__right_1, cls_one__le__inverse__iff_2, cls_add__le__cancel__left_1, cls_real__le__trans_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_of__real__0_0, cls_real__sqrt__lt__0__iff_1, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add, cls_real__mult__less__iff1_0, clsarity_RealDef__Oreal__Ring__and__Field_Odivision__ring, 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_inverse__1_0, cls_minus__le__self__iff_0, cls_inverse__negative__iff__negative_1, clsarity_nat__Orderings_Olinorder, cls_cos__le__one_0, cls_mult__nonpos__nonpos_0, cls_class__ringb_Onoteq__reduce_0, cls_comm__monoid__add_Omult__1__right_0, cls_minus__minus_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_abs__of__pos_0, cls_neg__less__iff__less_1, cls_t_I2_J_0, cls_add__cancel__21_1, cls_real__mult__le__cancel__iff2_0, clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs, cls_mult__le__cancel__left__pos_0, cls_sum__squares__ge__zero_0, cls_power__one_0, cls_add__nonpos__neg_0, clsarity_Complex__Ocomplex__OrderedGroup_Ogroup__add, cls_le__eq__neg_0, cls_left__inverse_0, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_add__left__cancel_0, cls_less__minus__iff_0, cls_mult_Ononneg__bounded_0, cls_minus__unique_0, cls_split__mult__neg__le_0, cls_inverse__nonnegative__iff__nonnegative_0, cls_sum__squares__le__zero__iff_1, cls_real__sqrt__le__1__iff_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono, cls_t_I1_J_0, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult, cls_add__nonneg__pos_0, cls_mult__less__cancel__left__disj_4, cls_class__ringb_Oadd__mul__solve_1, cls_mult__left_Opos__bounded_0, cls_mult__less__imp__less__left_0, cls_real__minus__mult__self__le_0, cls_real__sqrt__ge__0__iff_1, cls_mult__less__cancel__right__disj_3, cls_real__sqrt__lt__1__iff_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_mult__eq__0__iff_0, clsarity_nat__Ring__and__Field_Oordered__semidom, cls_real__sqrt__eq__iff_0, cls_abs__less__iff_2, clsarity_nat__OrderedGroup_Opordered__comm__monoid__add, cls_mult__mono_0, cls_abs__power__minus_0, cls_ab__left__minus_0, cls_neg__equal__iff__equal_0, cls_one__le__power_0, clsarity_nat__OrderedGroup_Omonoid__mult, cls_add__right__mono_0, cls_of__real__minus_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, clsarity_nat__Ring__and__Field_Oordered__semiring, cls_order__less__asym_0, cls_class__semiring_Osemiring__rules_I7_J_0, cls_abs__add__abs_0, cls_mult__left__mono__neg_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring, cls_linorder__not__less_0, cls_double__add__less__zero__iff__single__less__zero_0, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_mult_Ozero__left_0, cls_real__sqrt__eq__0__iff_0, cls_inverse__le__1__iff_1, 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, cls_class__semiring_Omul__c_0, cls_mult__pos__neg_0, cls_order__eq__refl_0, cls_inverse__eq__1__iff_1, 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_inverse__minus__eq_0, cls_mult__left__mono_0, cls_linorder__antisym__conv1_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero, clsarity_RealDef__Oreal__Ring__and__Field_Oring__no__zero__divisors, cls_real__sqrt__mult_0, cls_mult_Oadd__left_0, cls_linorder__antisym__conv2_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__by__zero, cls_add__cancel__end_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_class__semiring_Osemiring__rules_I12_J_0, cls_abs__eq__mult_0, cls_nonzero__abs__inverse_0, cls_mult__right_Oadd_0, cls_real__mult__is__one_2, cls_inverse__nonzero__iff__nonzero_0, cls_neg__0__le__iff__le_0, cls_of__real__eq__0__iff_0, cls_norm__one_0, cls_minus__less__iff_1, cls_inverse__nonpositive__iff__nonpositive_0, cls_inverse__nonnegative__iff__nonnegative_1, cls_minus__add__cancel_0, cls_real__less__def_0, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_real__sqrt__lt__1__iff_1, cls_xt1_I10_J_0, cls_add__nonneg__eq__0__iff_0, cls_mult__right_Obounded_0, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_no__zero__divisors_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict, cls_class__semiring_Osemiring__rules_I6_J_0, cls_neg__less__eq__nonneg_1, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_less__le__not__le_2, cls_add__left__mono_0, clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero, cls_le__minus__iff_0, cls_norm__ge__zero_0, cls_add__less__cancel__right_1, cls_neg__less__eq__nonneg_0, cls_mult__left_Ononneg__bounded_0, cls_not__less__iff__gr__or__eq_0, cls_complex__mod__minus__le__complex__mod_0, cls_zero__le__mult__iff_4, cls_power__gt1__lemma_0, clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring, cls_class__semiring_Osemiring__rules_I2_J_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_mult__1__right_0, cls_add__strict__left__mono_0, cls_real__sqrt__less__iff_1, cls_inverse__le__imp__le__neg_0, cls_real__le__refl_0, cls_mult__neg__pos_0, cls_norm__not__less__zero_0, cls_combine__common__factor_0, cls_estimate__by__abs_0, clsarity_nat__OrderedGroup_Ocomm__monoid__mult, cls_mult__le__0__iff_0, cls_add__le__less__mono_0, cls_mult__right__le__imp__le_0, cls_abs__eq__0_0, cls_of__real_Ozero_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring, cls_le__minus__iff_1, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add, cls_abs__ge__minus__self_0, cls_neg__le__0__iff__le_0, cls_le__eq__neg_1, cls_real__mult__less__mono2_0, cls_real__sqrt__ge__zero_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, cls_minus__mult__commute_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_le__imp__inverse__le_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra__1, cls_class__ringb_Onoteq__reduce_1, cls_class__semiring_Osemiring__rules_I19_J_0, clsarity_nat__Ring__and__Field_Opordered__cancel__semiring, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__algebra__1, cls_mult__le__cancel__left__neg_1, cls_inverse__negative__imp__negative_0, cls_real__sqrt__ge__1__iff_0, cls_class__semiring_Oadd__0_0, cls_power__less__power__Suc_0, cls_real__sqrt__minus_0, cls_zero__less__abs__iff_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_xt1_I8_J_0, cls_mult__left_Opos__bounded_1, cls_mult__le__cancel__left__pos_1, cls_one__le__inverse__iff_1, cls_mult__le__0__iff_1, cls_zero__less__mult__pos_0, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__add, cls_class__semiring_Osemiring__rules_I1_J_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_split__mult__pos__le_0, cls_sum__squares__le__zero__iff_2, 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_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs, clsarity_Complex__Ocomplex__OrderedGroup_Ocomm__monoid__add, cls_linorder__linear_0, cls_mult_Ominus__right_0, cls_of__real__1_0, cls_class__ringb_Oadd__mul__solve_0, cls_add__strict__mono_0, cls_neg__0__less__iff__less_0, cls_real__sqrt__gt__1__iff_1, cls_neg__less__0__iff__less_0, cls_sum__squares__eq__zero__iff_1, clsarity_nat__Ring__and__Field_Omult__mono, cls_neg__equal__0__iff__equal_0, clsarity_RealDef__Oreal__Ring__and__Field_Oring__1, cls_abs__idempotent_0, cls_mult__le__0__iff_4, clsarity_Complex__Ocomplex__RealVector_Oreal__algebra__1, cls_real__mult__less__iff1_1, cls_zero__less__two_0, cls_le__minus__self__iff_1, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__comm__semiring__strict, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring__1, cls_less__add__one_0, cls_not__leE_0, cls_real__sqrt__le__0__iff_0, cls_mult__less__cancel__right__disj_2, cls_zero__less__power_0, cls_minus__le__self__iff_1, cls_order__antisym_0, cls_order__trans_0, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_mult_Ononneg__bounded_1, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__div__algebra, cls_mult__left__less__imp__less_0, cls_mult__strict__left__mono_0, cls_class__semiring_Omul__d_0, cls_neg__equal__zero_1, cls_power__abs_0, cls_real__mult__order_0, cls_add__cancel__21_0, cls_nonzero__inverse__minus__eq_0, cls_sum__squares__gt__zero__iff_2, cls_of__real__mult_0, cls_class__semiring_Osemiring__rules_I5_J_0, cls_abs__minus__cancel_0, cls_linorder__antisym__conv1_1, cls_split__mult__pos__le_1, cls_no__zero__divirors__neq0_0, cls_inverse__nonzero__iff__nonzero_1, cls_mult__right_Ominus_0, cls_inverse__le__1__iff_0, cls_mult__le__0__iff_5, clsarity_RealDef__Oreal__RealVector_Oreal__normed__vector, cls_mult__strict__mono_H_0, cls_zero__neq__one_0, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_real__mult__left__cancel_0, cls_abs__ge__zero_0, clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add, cls_inverse__add_0, cls_abs__if_1, cls_inverse__eq__1__iff_0, cls_abs__eq__mult_3, cls_real__mult__right__cancel_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add, cls_linorder__not__le_1, cls_less__1__mult_0, clsarity_Complex__Ocomplex__OrderedGroup_Oab__group__add, cls_less__imp__inverse__less_0, clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult, cls_zero__le__power__abs_0, cls_add__less__cancel__right_0, cls_minus__less__iff_0, cls_mult__less__cancel__right__disj_5, cls_sin__zero_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ozero__neq__one, cls_real__sqrt__gt__zero_0, cls_inverse__less__1__iff_0, cls_abs__ge__self_0, clsarity_Complex__Ocomplex__Ring__and__Field_Odivision__ring, cls_real__sqrt__ge__one_0, clsarity_nat__Orderings_Opreorder, cls_class__semiring_Omul__a_0, cls_not__less__iff__gr__or__eq_1, cls_neg__0__equal__iff__equal_1, cls_power__inverse_0, cls_zero__le__square_0, cls_equation__minus__iff_0, cls_less__minus__iff_1, cls_zero__less__double__add__iff__zero__less__single__add_1, cls_add__increasing_0, cls_mult__nonneg__nonpos_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oidom, cls_right__inverse_0, cls_real__sqrt__less__iff_0, cls_less__eq__neg__nonpos_1, cls_inverse__positive__iff__positive_0, clsarity_Complex__Ocomplex__OrderedGroup_Ocancel__ab__semigroup__add, cls_order__le__neq__trans_0, cls_class__semiring_Omul__1_0, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_inverse__positive__iff__positive_1, cls_class__ringb_Oadd__scale__eq__noteq_0, cls_real__sum__squares__cancel__a_1, cls_inverse__unique_0, cls_order__eq__iff_2, cls_linorder__neqE__ordered__idom_0, cls_double__add__le__zero__iff__single__add__le__zero_1, cls_class__ringb_Oadd__cancel_0, cls_one__less__inverse__iff_2, cls_less__le__not__le_1, cls_add__nonneg__eq__0__iff_1, clsarity_Complex__Ocomplex__Ring__and__Field_Oring, cls_class__semiring_Osemiring__rules_I23_J_0, cls_abs__of__nonpos_0, cls_not__square__less__zero_0, cls_linorder__antisym__conv3_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__comm__monoid__add, clsarity_nat__OrderedGroup_Oab__semigroup__mult, clsarity_RealDef__Oreal__Ring__and__Field_Oidom, cls_mult__left__le__one__le_0, cls_add__nonpos__nonpos_0, cls_sin__minus_0, cls_abs__less__iff_0, cls_class__semiring_Osemiring__rules_I3_J_0, cls_one__le__inverse__iff_0, cls_mult__eq__0__iff_2, cls_sum__squares__gt__zero__iff_1, cls_order__neq__le__trans_0, cls_add__nonneg__nonneg_0, cls_mult_Opos__bounded_1, cls_class__ring_Oneg__mul_0, cls_neg__le__0__iff__le_1, cls_mult__strict__left__mono__comm_0, cls_order__antisym__conv_0, cls_abs__le__D2_0, cls_of__real_Ominus_0, clsarity_nat__Ring__and__Field_Osemiring, cls_eq__neg__iff__add__eq__0_1, cls_mult__mono_H_0, cls_class__ringb_Oadd__r0__iff_0, cls_mult__right_Ononneg__bounded_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_abs__mult__self_0, cls_mult__less__cancel__left__neg_1, cls_division__ring__inverse__add_0, cls_even__less__0__iff_1, cls_complex__Re__le__cmod_0, cls_le__imp__neg__le_0, cls_not__real__square__gt__zero_1, cls_linorder__less__linear_0, clsarity_nat__Power_Opower, cls_zero__le__mult__iff_5, cls_inverse__negative__iff__negative_0, cls_abs__mult__pos_0, cls_class__semiring_Osemiring__rules_I11_J_0, clsarity_RealDef__Oreal__Ring__and__Field_Ofield, cls_order__less__le_2, cls_mult__less__cancel__left__pos_1, cls_abs__not__less__zero_0, cls_add__strict__increasing_0, cls_real__sqrt__le__iff_0, cls_abs__le__mult_0, cls_nonzero__inverse__inverse__eq_0, cls_power__mult__distrib_0, cls_mult_Ominus__left_0, cls_real__sqrt__one_0, cls_norm__mult_0, cls_neg__0__less__iff__less_1, cls_real__sqrt__gt__1__iff_0, cls_nonzero__inverse__eq__imp__eq_0, cls_cos__zero_0, cls_zero__le__mult__iff_1, clsarity_Complex__Ocomplex__RealVector_Oreal__normed__vector, cls_power__commutes_0, cls_abs__if__lattice_1, cls_minus__mult__left_0, cls_xt1_I11_J_0, cls_norm__eq__zero_0, cls_add__neg__neg_0, cls_abs__triangle__ineq_0, cls_mult__le__0__iff_2, cls_mult__le__cancel__left__neg_0, cls_zero__less__abs__iff_1, cls_double__eq__0__iff_0, cls_one__neq__zero_0, clsarity_RealDef__Oreal__Ring__and__Field_Osemiring, cls_class__semiring_Osemiring__rules_I18_J_0, cls_mult__right__le__one__le_0, cls_mult__right_Opos__bounded_1, cls_neg__less__0__iff__less_1, cls_add__minus__cancel_0, cls_real__le__antisym_0, cls_xt1_I6_J_0, cls_double__compl_0, cls_zero__less__mult__pos2_0, cls_mult__left_Ominus_0, cls_mult__1_0, cls_mult_Oadd__right_0, clsarity_Complex__Ocomplex__OrderedGroup_Omonoid__add, cls_comm__monoid__add_Omult__left__commute_0, cls_mult__right__mono__neg_0, cls_abs__mult_0, cls_neg__equal__zero_0, cls_real__sqrt__ge__1__iff_1, cls_sum__squares__eq__zero__iff_2, cls_positive__imp__inverse__positive_0, cls_le__add__right__mono_0, cls_minus__mult__right_0, cls_inverse__inverse__eq_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_mult__less__cancel__left__disj_3, cls_norm__mult__ineq_0, clsarity_nat__Ring__and__Field_Omult__mono1, cls_minus__le__iff_1, cls_mult__less__cancel__right__disj_4, cls_mult__1__left_0, clsarity_RealDef__Oreal__Ring__and__Field_Ocomm__semiring, cls_one__less__inverse__iff_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add, cls_real__sum__squares__cancel__a_0, cls_mult__zero__left_0, cls_of__real__eq__iff_0, cls_linorder__not__le_0, cls_real__sqrt__eq__1__iff_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__1__no__zero__divisors, cls_double__add__less__zero__iff__single__less__zero_1, cls_real__sqrt__le__1__iff_1, cls_inverse__less__1__iff_1, cls_abs__if_0, cls_real__zero__not__eq__one_0, cls_comm__monoid__add_Omult__1_0, cls_norm__le__zero__iff_1, cls_real__mult__is__one_0, cls_less__eq__neg__nonpos_0, cls_norm__mult__less_0, clsarity_Complex__Ocomplex__OrderedGroup_Oab__semigroup__mult, cls_order__less__irrefl_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, clsarity_nat__Ring__and__Field_Opordered__semiring, cls_add__nonneg__eq__0__iff_2, cls_power__eq__0__iff_0, cls_class__semiring_Oadd__c_0, cls_mult__pos__pos_0, cls_neg__0__equal__iff__equal_0, cls_mult__left__le__imp__le_0, cls_neg__le__iff__le_0, cls_real__sqrt__gt__0__iff_0, cls_less__minus__self__iff_1, cls_one__less__inverse__iff_1, cls_real__mult__1_0, cls_mult__strict__right__mono__neg_0, clsarity_nat__Ring__and__Field_Ono__zero__divisors, cls_mult__right_Ononneg__bounded_1, cls_inverse__zero_0, cls_inverse__less__imp__less__neg_0, cls_norm__ratiotest__lemma_0, cls_add__pos__pos_0, cls_add__mono_0, cls_mult__right__less__imp__less_0, cls_sum__squares__gt__zero__iff_0, clsarity_Complex__Ocomplex__Ring__and__Field_Osemiring, cls_class__semiring_Osemiring__rules_I8_J_0, cls_add__neg__nonpos_0, cls_power__less__imp__less__base_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__idom, cls_less__minus__self__iff_0, clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add, cls_inverse__le__imp__le_0, cls_equation__minus__iff_1, cls_cos__one__sin__zero_0, cls_real__sqrt__eq__zero__cancel_0, clsarity_Complex__Ocomplex__Power_Opower, cls_real__mult__commute_0, cls_class__semiring_Osemiring__rules_I24_J_0, cls_add__less__cancel__left_0, cls_abs__one_0, cls_mult__less__cancel__left__disj_2, cls_minus__add_0, clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult, cls_real__mult__le__cancel__iff1_1, cls_field__inverse_0, cls_class__semiring_Opwr__mul_0, cls_abs__le__zero__iff_1, cls_abs__eq__0_1, cls_mult__less__cancel__right__disj_1, cls_real__sqrt__le__0__iff_1, cls_abs__leI_0, clsarity_RealDef__Oreal__Orderings_Oorder, cls_abs__inverse_0, cls_right__minus_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_inverse__mult__distrib_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring, cls_power__minus_0, cls_mult__eq__0__iff_1, cls_add__less__le__mono_0, cls_zero__le__power_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom, cls_real__less__def_2, cls_inverse__positive__imp__positive_0, clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add, cls_norm__le__zero__iff_0, cls_nonzero__inverse__mult__distrib_0, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring__1, cls_nonzero__power__inverse_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring, cls_inverse__less__imp__less_0, cls_order__less__imp__le_0, cls_abs__le__D1_0, cls_minus__equation__iff_1, cls_abs__eq__mult_2, cls_not__real__square__gt__zero_0, cls_eq__neg__iff__add__eq__0_0, cls_mult_Obounded_0, cls_le__imp__inverse__le__neg_0, cls_norm__minus__cancel_0, clsarity_nat__OrderedGroup_Ocomm__monoid__add, clsarity_Complex__Ocomplex__Ring__and__Field_Ono__zero__divisors, cls_zero__less__norm__iff_0, cls_mult__idem_0, cls_monoid__add__class_Oadd__0__right_0, cls_real__sqrt__lt__0__iff_0, cls_add__strict__increasing2_0, clsarity_RealDef__Oreal__Int_Onumber__ring, cls_minus__mult__minus_0, clsarity_nat__Ring__and__Field_Omult__zero, cls_xt1_I7_J_0, cls_inverse__nonpositive__iff__nonpositive_1, cls_not__one__le__zero_0, cls_mult__less__le__imp__less_0, clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, cls_mult_Opos__bounded_0, cls_square__eq__iff_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_mult__le__0__iff_3, cls_real__sqrt__not__eq__zero_0, cls_mult__neg__neg_0, cls_linorder__not__less_1, cls_mult__less__cancel__left__neg_0, cls_class__semiring_Osemiring__rules_I4_J_0, clsarity_Complex__Ocomplex__Int_Onumber__ring, cls_add__le__cancel__left_0, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, clsarity_Complex__Ocomplex__Ring__and__Field_Ocomm__semiring, cls_mult__right_Opos__bounded_0, cls_power__Suc__less_0, cls_neg__less__iff__less_0, cls_even__less__0__iff_0, cls_mult__left_Oadd_0, cls_sum__squares__le__zero__iff_0, cls_real__sqrt__ge__0__iff_0, cls_add__le__cancel__right_0, cls_split__mult__neg__le_1, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict, cls_power__mono_0, cls_zero__le__mult__iff_2, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__strict__left__mono__neg_0, clsarity_Complex__Ocomplex__Ring__and__Field_Oring__no__zero__divisors, cls_abs__of__neg_0, cls_abs__less__iff_1, cls_mult__less__cancel__left__pos_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring__abs, cls_cos__minus_0, cls_class__semiring_Osemiring__rules_I22_J_0, cls_real__sqrt__le__iff_1
% 60.98/12.38  % No. of inferences in proof: 1357
% 60.98/12.38  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 11900 ms resp. 11068 ms w/o parsing
% 61.22/12.57  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 61.22/12.57  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------