TSTP Solution File: SWV603-1 by Leo-III---1.7.12

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Leo-III---1.7.12
% Problem  : SWV603-1 : TPTP v8.2.0. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : run_Leo-III %s %d

% Computer : n019.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 : Tue May 21 05:47:27 EDT 2024

% Result   : Unsatisfiable 15.17s 4.64s
% Output   : Refutation 16.48s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    2
%            Number of leaves      : 1119
% Syntax   : Number of formulae    : 2154 ( 433 unt;  85 typ;   0 def)
%            Number of atoms       : 6339 (1092 equ;   0 cnn)
%            Maximal formula atoms :    7 (   3 avg)
%            Number of connectives : 35318 (3910   ~;4270   |;   0   &;27138   @)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (  10 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   98 (  98   >;   0   *;   0   +;   0  <<)
%            Number of symbols     :   87 (  85 usr;   6 con; 0-3 aty)
%            Number of variables   : 5120 (   0   ^5120   !;   0   ?;5120   :)

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

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

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

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

thf(c_Int_OBit0_type,type,
    c_Int_OBit0: $i > $i ).

thf(c_Int_OBit1_type,type,
    c_Int_OBit1: $i > $i ).

thf(c_Int_OPls_type,type,
    c_Int_OPls: $i ).

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

thf(c_Transcendental_Opi_type,type,
    c_Transcendental_Opi: $i ).

thf(c_RealDef_Oreal_type,type,
    c_RealDef_Oreal: $i > $i > $i ).

thf(v_n_type,type,
    v_n: $i ).

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

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

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

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

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

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

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

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(c_HOL_Ominus__class_Ominus_type,type,
    c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).

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

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

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

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

thf(class_OrderedGroup_Oordered__ab__group__add_type,type,
    class_OrderedGroup_Oordered__ab__group__add: $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_Oring_type,type,
    class_Ring__and__Field_Oring: $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_Orderings_Oorder_type,type,
    class_Orderings_Oorder: $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__group__add_type,type,
    class_OrderedGroup_Opordered__ab__group__add: $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_Ring__and__Field_Oordered__semidom_type,type,
    class_Ring__and__Field_Oordered__semidom: $i > $o ).

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

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

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

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

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

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

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

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

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

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

thf(c_Transcendental_Otan_type,type,
    c_Transcendental_Otan: $i > $i ).

thf(c_Transcendental_Oarctan_type,type,
    c_Transcendental_Oarctan: $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

thf(class_Int_Oring__char__0_type,type,
    class_Int_Oring__char__0: $i > $o ).

thf(c_Parity_Oeven__odd__class_Oeven_type,type,
    c_Parity_Oeven__odd__class_Oeven: $i > $i > $o ).

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

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

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

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

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

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

thf(c_Transcendental_Osko__Transcendental__Xtan__total__pi4__1__1_type,type,
    c_Transcendental_Osko__Transcendental__Xtan__total__pi4__1__1: $i > $i ).

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

thf(class_RealVector_Oreal__field_type,type,
    class_RealVector_Oreal__field: $i > $o ).

thf(c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1_type,type,
    c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1: $i > $i ).

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

thf(c_FFT__Mirabelle_Oroot_type,type,
    c_FFT__Mirabelle_Oroot: $i > $i ).

thf(c_Complex_Ocis_type,type,
    c_Complex_Ocis: $i > $i ).

thf(hAPP_type,type,
    hAPP: $i > $i > $i ).

thf(888,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__squared__diff__one__factored_0) ).

thf(3021,plain,
    ! [A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[888]) ).

thf(158,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(1411,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)],[158]) ).

thf(181,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(1469,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)],[181]) ).

thf(569,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(2336,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)],[569]) ).

thf(249,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq2_0) ).

thf(1633,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).

thf(218,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(1559,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)],[218]) ).

thf(291,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(1729,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)],[291]) ).

thf(85,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_1) ).

thf(1237,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).

thf(630,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_1) ).

thf(2463,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).

thf(638,axiom,
    ( ( c_Transcendental_Osin @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__45_0) ).

thf(2480,plain,
    ( ( c_Transcendental_Osin @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).

thf(674,axiom,
    class_Orderings_Opreorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Opreorder) ).

thf(2559,plain,
    class_Orderings_Opreorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).

thf(667,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono__neg_0) ).

thf(2544,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).

thf(567,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_4) ).

thf(2331,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).

thf(388,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__1_0) ).

thf(1950,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).

thf(543,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__monotone_H_0) ).

thf(2280,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).

thf(274,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(1686,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)],[274]) ).

thf(2,negated_conjecture,
    ( ( c_HOL_Oabs__class_Oabs @ ( c_Transcendental_Ocos @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ v_n @ tc_nat ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).

thf(1036,plain,
    ( ( c_HOL_Oabs__class_Oabs @ ( c_Transcendental_Ocos @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ v_n @ tc_nat ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).

thf(706,axiom,
    ! [A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__arith_I112_J_0) ).

thf(2630,plain,
    ! [A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).

thf(229,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ C @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__add__cancel_0) ).

thf(1586,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ C @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).

thf(194,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(1501,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)],[194]) ).

thf(355,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_2) ).

thf(1879,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).

thf(126,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_NthRoot_Osqrt @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__real__sqrt__sumsq_0) ).

thf(1337,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_NthRoot_Osqrt @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).

thf(287,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__left_0) ).

thf(1718,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).

thf(57,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(1168,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)],[57]) ).

thf(556,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(2306,plain,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).

thf(904,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(3053,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)],[904]) ).

thf(448,axiom,
    ( ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
   != ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__neq__two_0) ).

thf(2072,plain,
    ( ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
   != ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).

thf(307,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(1767,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)],[307]) ).

thf(691,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(2595,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)],[691]) ).

thf(646,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_5) ).

thf(2499,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).

thf(74,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__self_0) ).

thf(1211,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).

thf(653,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal )
      = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__mult__distrib_0) ).

thf(2512,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal )
      = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ C @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).

thf(377,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_4) ).

thf(1924,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).

thf(1029,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(3317,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)],[1029]) ).

thf(107,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ab__diff__minus_0) ).

thf(1290,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).

thf(15,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__le__0__iff_0) ).

thf(1068,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).

thf(588,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(2381,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)],[588]) ).

thf(98,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(1269,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)],[98]) ).

thf(318,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__eq_H_0) ).

thf(1793,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).

thf(4,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(1041,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)],[4]) ).

thf(59,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(1173,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)],[59]) ).

thf(345,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(1855,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)],[345]) ).

thf(70,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(1200,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)],[70]) ).

thf(300,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(1750,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)],[300]) ).

thf(967,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__add) ).

thf(3185,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[967]) ).

thf(468,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__frac_0) ).

thf(2117,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).

thf(233,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_5) ).

thf(1596,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).

thf(462,axiom,
    ! [C: $i,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_Odivide @ B @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__divide_0) ).

thf(2104,plain,
    ! [C: $i,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_Odivide @ B @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).

thf(788,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Oinverse__class_Odivide @ B @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__divide__square__eq_0) ).

thf(2808,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Oinverse__class_Odivide @ B @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[788]) ).

thf(202,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_4) ).

thf(1522,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).

thf(594,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_6) ).

thf(2395,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).

thf(835,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
       != ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
      | ( B
        = ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_0) ).

thf(2908,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
       != ( c_Int_Onumber__class_Onumber__of @ D @ A ) )
      | ( B
        = ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[835]) ).

thf(442,axiom,
    ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__3over2__pi_0) ).

thf(2062,plain,
    ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).

thf(857,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Transcendental_Oarctan @ A ) @ ( c_Transcendental_Oarctan @ B ) @ tc_RealDef_Oreal )
        = ( c_Transcendental_Oarctan @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan__add_0) ).

thf(2953,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Transcendental_Oarctan @ A ) @ ( c_Transcendental_Oarctan @ B ) @ tc_RealDef_Oreal )
        = ( c_Transcendental_Oarctan @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[857]) ).

thf(689,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(2590,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)],[689]) ).

thf(153,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_0) ).

thf(1401,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).

thf(854,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__monotone_0) ).

thf(2947,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[854]) ).

thf(222,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(1569,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)],[222]) ).

thf(926,axiom,
    class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__field) ).

thf(3098,plain,
    class_RealVector_Oreal__normed__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[926]) ).

thf(17,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_2) ).

thf(1073,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).

thf(883,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_2) ).

thf(3012,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[883]) ).

thf(72,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(1205,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)],[72]) ).

thf(544,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(2282,plain,
    class_Ring__and__Field_Ono__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).

thf(231,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_1) ).

thf(1591,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).

thf(239,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_2) ).

thf(1608,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).

thf(944,axiom,
    class_Ring__and__Field_Omult__zero @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__zero) ).

thf(3135,plain,
    class_Ring__and__Field_Omult__zero @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[944]) ).

thf(899,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_6) ).

thf(3044,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[899]) ).

thf(623,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(2448,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).

thf(478,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(2141,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)],[478]) ).

thf(304,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_3) ).

thf(1761,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).

thf(390,axiom,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semidom) ).

thf(1954,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).

thf(481,axiom,
    class_Orderings_Oorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).

thf(2146,plain,
    class_Orderings_Oorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).

thf(176,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(1458,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)],[176]) ).

thf(696,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(2607,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)],[696]) ).

thf(731,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_8) ).

thf(2686,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).

thf(302,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_1) ).

thf(1756,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).

thf(115,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ 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 ) @ C @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_2) ).

thf(1310,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ 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 ) @ C @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).

thf(880,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(3004,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)],[880]) ).

thf(430,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_0) ).

thf(2035,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).

thf(757,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Otan @ ( c_HOL_Oplus__class_Oplus @ A @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Otan @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__periodic__pi_0) ).

thf(2740,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Otan @ ( c_HOL_Oplus__class_Oplus @ A @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Otan @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[757]) ).

thf(840,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(2918,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)],[840]) ).

thf(350,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(1867,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)],[350]) ).

thf(961,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__mult) ).

thf(3175,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[961]) ).

thf(55,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_3) ).

thf(1164,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).

thf(414,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(1999,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)],[414]) ).

thf(408,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_4) ).

thf(1988,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).

thf(628,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__le__div__pos_0) ).

thf(2459,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).

thf(196,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(1507,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)],[196]) ).

thf(79,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_Int_Onumber @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_0) ).

thf(1222,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_Int_Onumber @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).

thf(27,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_0) ).

thf(1095,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).

thf(68,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(1196,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)],[68]) ).

thf(298,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_3) ).

thf(1746,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).

thf(371,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(1914,plain,
    class_Ring__and__Field_Opordered__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).

thf(518,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_7) ).

thf(2227,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).

thf(170,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(1441,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)],[170]) ).

thf(6,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(1046,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)],[6]) ).

thf(1012,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( B
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_3) ).

thf(3281,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( B
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1012]) ).

thf(452,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_0) ).

thf(2082,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).

thf(138,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(1366,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)],[138]) ).

thf(655,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(2516,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)],[655]) ).

thf(793,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_2) ).

thf(2819,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[793]) ).

thf(662,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__neg_0) ).

thf(2531,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).

thf(816,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(2869,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[816]) ).

thf(859,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__eq__0__iff_1) ).

thf(2957,plain,
    ! [A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[859]) ).

thf(574,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_5) ).

thf(2348,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).

thf(748,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_0) ).

thf(2723,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).

thf(643,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__diff__distrib__number__of_0) ).

thf(2491,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).

thf(669,axiom,
    ( ( c_Transcendental_Osin @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__60_0) ).

thf(2548,plain,
    ( ( c_Transcendental_Osin @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).

thf(313,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(1782,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)],[313]) ).

thf(257,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(1650,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)],[257]) ).

thf(375,axiom,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add) ).

thf(1921,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).

thf(946,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(3140,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)],[946]) ).

thf(289,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_0) ).

thf(1724,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).

thf(445,axiom,
    class_Int_Onumber @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber) ).

thf(2067,plain,
    class_Int_Onumber @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).

thf(205,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(1529,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)],[205]) ).

thf(397,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oabs__class_Oabs @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rabs__ratiotest__lemma_0) ).

thf(1967,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oabs__class_Oabs @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).

thf(476,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_1) ).

thf(2136,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).

thf(281,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ E @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).

thf(1703,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ C @ B @ A )
      | ~ ( c_lessequals @ E @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).

thf(245,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(1623,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)],[245]) ).

thf(92,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(1254,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)],[92]) ).

thf(715,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_4) ).

thf(2654,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).

thf(565,axiom,
    class_Int_Oring__char__0 @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Oring__char__0) ).

thf(2328,plain,
    class_Int_Oring__char__0 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).

thf(892,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(3029,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)],[892]) ).

thf(1009,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(3275,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)],[1009]) ).

thf(721,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(2667,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)],[721]) ).

thf(900,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ B ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ B ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__diff2_0) ).

thf(3046,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ B ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ B ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[900]) ).

thf(333,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(1826,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)],[333]) ).

thf(921,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(3089,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)],[921]) ).

thf(631,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__left__mono__neg_0) ).

thf(2466,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).

thf(739,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_0) ).

thf(2703,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).

thf(157,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(1409,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)],[157]) ).

thf(977,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(3204,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)],[977]) ).

thf(1003,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(3263,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)],[1003]) ).

thf(106,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(1287,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)],[106]) ).

thf(984,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_8) ).

thf(3221,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[984]) ).

thf(791,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Ocos @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__periodic_0) ).

thf(2814,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Ocos @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[791]) ).

thf(406,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oinverse__class_Odivide @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Oinverse__class_Odivide @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__minus__half__eq_0) ).

thf(1985,plain,
    ! [A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Oinverse__class_Odivide @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Oinverse__class_Odivide @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).

thf(737,axiom,
    ! [A: $i] :
      ( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
      | ( ( c_Transcendental_Ocos @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ A @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__zero__iff_5) ).

thf(2698,plain,
    ! [A: $i] :
      ( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
      | ( ( c_Transcendental_Ocos @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ A @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).

thf(942,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(3131,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)],[942]) ).

thf(262,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(1660,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)],[262]) ).

thf(110,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Deriv_Oadd__diff__add_0) ).

thf(1298,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).

thf(367,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ B ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ B ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__diff2_0) ).

thf(1907,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ B ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ B ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).

thf(647,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_2) ).

thf(2501,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).

thf(620,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Osin @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__add_0) ).

thf(2444,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Osin @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).

thf(96,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(1264,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)],[96]) ).

thf(514,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(2217,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)],[514]) ).

thf(121,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(1323,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)],[121]) ).

thf(949,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(3148,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)],[949]) ).

thf(499,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_6) ).

thf(2185,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).

thf(175,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( 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_Odiff__right_0) ).

thf(1455,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( 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)],[175]) ).

thf(336,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_4) ).

thf(1832,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).

thf(830,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(2897,plain,
    class_Ring__and__Field_Opordered__cancel__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[830]) ).

thf(66,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_5) ).

thf(1191,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).

thf(178,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(1462,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)],[178]) ).

thf(898,axiom,
    class_OrderedGroup_Oab__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add) ).

thf(3043,plain,
    class_OrderedGroup_Oab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[898]) ).

thf(679,axiom,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__60_0) ).

thf(2571,plain,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).

thf(578,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(2356,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)],[578]) ).

thf(212,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(1545,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)],[212]) ).

thf(376,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(1922,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)],[376]) ).

thf(144,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(1379,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)],[144]) ).

thf(48,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__neg_0) ).

thf(1147,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).

thf(89,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__bound__lemma_0) ).

thf(1247,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).

thf(770,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(2767,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)],[770]) ).

thf(845,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_4) ).

thf(2929,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[845]) ).

thf(487,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ A @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal ) @ 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_lemma__real__divide__sqrt__less_0) ).

thf(2158,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ A @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal ) @ 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)],[487]) ).

thf(253,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__divide_0) ).

thf(1641,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).

thf(964,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Ocos @ A )
      = ( c_Transcendental_Osin @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__sin__eq_0) ).

thf(3180,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Ocos @ A )
      = ( c_Transcendental_Osin @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[964]) ).

thf(353,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lim_Ominus__diff__minus_0) ).

thf(1875,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).

thf(988,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(3231,plain,
    class_Ring__and__Field_Omult__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[988]) ).

thf(663,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(2533,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)],[663]) ).

thf(342,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__add__iff_1) ).

thf(1847,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).

thf(927,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__1__iff_0) ).

thf(3099,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[927]) ).

thf(321,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(1800,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)],[321]) ).

thf(584,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(2373,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)],[584]) ).

thf(131,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(1347,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)],[131]) ).

thf(296,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(1741,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)],[296]) ).

thf(152,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(1398,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)],[152]) ).

thf(1026,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__pos_0) ).

thf(3312,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1026]) ).

thf(380,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(1931,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)],[380]) ).

thf(884,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_9) ).

thf(3014,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[884]) ).

thf(751,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add) ).

thf(2730,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).

thf(554,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__Numeral0_0) ).

thf(2301,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).

thf(328,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(1815,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)],[328]) ).

thf(191,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__diff__le__0_1) ).

thf(1494,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_lessequals @ B @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).

thf(83,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(1232,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)],[83]) ).

thf(1006,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(3268,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)],[1006]) ).

thf(1001,axiom,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__pi__half_0) ).

thf(3258,plain,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1001]) ).

thf(627,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_3) ).

thf(2456,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).

thf(516,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ B @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__2_0) ).

thf(2222,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ B @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).

thf(426,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__squares__cancel2_0) ).

thf(2027,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).

thf(326,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(1811,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)],[326]) ).

thf(1017,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(3295,plain,
    class_Ring__and__Field_Ozero__neq__one @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1017]) ).

thf(125,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(1334,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)],[125]) ).

thf(43,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(1136,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)],[43]) ).

thf(50,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(1151,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)],[50]) ).

thf(429,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__cos__le__one_0) ).

thf(2034,plain,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).

thf(227,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(1581,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)],[227]) ).

thf(63,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(1183,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)],[63]) ).

thf(264,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(1664,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)],[264]) ).

thf(782,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Int_Oring__char__0 @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__number__of_0) ).

thf(2794,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Int_Oring__char__0 @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[782]) ).

thf(625,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(2451,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)],[625]) ).

thf(522,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(2236,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)],[522]) ).

thf(349,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(1864,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)],[349]) ).

thf(470,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(2122,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)],[470]) ).

thf(334,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(1828,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)],[334]) ).

thf(402,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__mult__self__sum__ge__zero_0) ).

thf(1978,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).

thf(549,axiom,
    class_OrderedGroup_Omonoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add) ).

thf(2291,plain,
    class_OrderedGroup_Omonoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).

thf(146,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(1383,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)],[146]) ).

thf(394,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_1) ).

thf(1960,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).

thf(1015,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__diff__distrib__number__of_0) ).

thf(3290,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1015]) ).

thf(774,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_half__gt__zero_0) ).

thf(2777,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[774]) ).

thf(951,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__monotone__minus__pi__0_0) ).

thf(3152,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[951]) ).

thf(651,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_1) ).

thf(2508,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).

thf(440,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_4) ).

thf(2058,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).

thf(582,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_2) ).

thf(2367,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).

thf(143,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(1377,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)],[143]) ).

thf(358,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(1886,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)],[358]) ).

thf(659,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__divide_0) ).

thf(2523,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).

thf(204,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(1526,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)],[204]) ).

thf(994,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oabs__class_Oabs @ ( c_RealDef_Oreal @ A @ tc_nat ) @ tc_RealDef_Oreal )
      = ( c_RealDef_Oreal @ A @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__real__of__nat__cancel_0) ).

thf(3243,plain,
    ! [A: $i] :
      ( ( c_HOL_Oabs__class_Oabs @ ( c_RealDef_Oreal @ A @ tc_nat ) @ tc_RealDef_Oreal )
      = ( c_RealDef_Oreal @ A @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[994]) ).

thf(986,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(3226,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)],[986]) ).

thf(786,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(2804,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)],[786]) ).

thf(235,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__add__iff_0) ).

thf(1600,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).

thf(87,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(1242,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)],[87]) ).

thf(593,axiom,
    ! [A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Pls_0) ).

thf(2392,plain,
    ! [A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).

thf(746,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__numeral__1__right_0) ).

thf(2718,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).

thf(220,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(1564,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)],[220]) ).

thf(768,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(2762,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)],[768]) ).

thf(701,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(2618,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)],[701]) ).

thf(970,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(3189,plain,
    class_Ring__and__Field_Oordered__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[970]) ).

thf(772,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(2772,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)],[772]) ).

thf(953,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_4) ).

thf(3157,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[953]) ).

thf(525,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__average__minus__second_0) ).

thf(2242,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).

thf(130,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(1345,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)],[130]) ).

thf(763,axiom,
    ! [A: $i] :
      ( ( ( c_Transcendental_Ocos @ A )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1 @ A ) @ tc_nat ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__zero__lemma_0) ).

thf(2750,plain,
    ! [A: $i] :
      ( ( ( c_Transcendental_Ocos @ A )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ~ ( c_Parity_Oeven__odd__class_Oeven @ ( c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1 @ A ) @ tc_nat ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[763]) ).

thf(155,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_4) ).

thf(1405,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).

thf(278,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(1696,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)],[278]) ).

thf(966,axiom,
    c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__ge__zero_0) ).

thf(3184,plain,
    c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[966]) ).

thf(686,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(2586,plain,
    class_Ring__and__Field_Oordered__semidom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).

thf(419,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_7) ).

thf(2011,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).

thf(987,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_7) ).

thf(3229,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[987]) ).

thf(635,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_1) ).

thf(2473,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).

thf(276,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(1691,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)],[276]) ).

thf(712,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(2646,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).

thf(113,axiom,
    ! [B: $i,A: $i] :
      ( A
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__diff__eq_H_1) ).

thf(1306,plain,
    ! [B: $i,A: $i] :
      ( A
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).

thf(968,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(3186,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)],[968]) ).

thf(127,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff2_1) ).

thf(1338,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).

thf(434,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(2047,plain,
    class_Ring__and__Field_Opordered__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).

thf(755,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(2737,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)],[755]) ).

thf(710,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_0) ).

thf(2641,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).

thf(702,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__eq__diff_1) ).

thf(2621,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).

thf(834,axiom,
    ! [A: $i] :
      ( ( c_Int_OBit1 @ A )
     != c_Int_OPls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I46_J_0) ).

thf(2905,plain,
    ! [A: $i] :
      ( ( c_Int_OBit1 @ A )
     != c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[834]) ).

thf(895,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(3037,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)],[895]) ).

thf(237,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(1604,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)],[237]) ).

thf(842,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_6) ).

thf(2922,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[842]) ).

thf(1021,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_7) ).

thf(3301,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1021]) ).

thf(1022,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(3303,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)],[1022]) ).

thf(581,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_4) ).

thf(2364,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).

thf(490,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(2164,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)],[490]) ).

thf(372,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(1915,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)],[372]) ).

thf(283,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__def_0) ).

thf(1708,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).

thf(457,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Oinverse__class_Odivide @ A @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__2__times__iff_0) ).

thf(2093,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Oinverse__class_Odivide @ A @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).

thf(520,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_8) ).

thf(2232,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).

thf(557,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Osin @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ B )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ A )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__tan__eq_0) ).

thf(2307,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Osin @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ B )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ A )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).

thf(688,axiom,
    class_Ring__and__Field_Omult__mono1 @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono1) ).

thf(2589,plain,
    class_Ring__and__Field_Omult__mono1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).

thf(25,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(1091,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)],[25]) ).

thf(693,axiom,
    ( ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
   != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__neq__zero_0) ).

thf(2601,plain,
    ( ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
   != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).

thf(529,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_0) ).

thf(2249,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).

thf(666,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(2541,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)],[666]) ).

thf(134,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).

thf(1355,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).

thf(38,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(1123,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)],[38]) ).

thf(270,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_HOL_Oord__class_Oless @ D @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).

thf(1676,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_HOL_Oord__class_Oless @ D @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).

thf(482,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_8) ).

thf(2147,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).

thf(265,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(1666,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)],[265]) ).

thf(188,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ring_Osub__add_0) ).

thf(1487,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).

thf(849,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono__neg_0) ).

thf(2937,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[849]) ).

thf(952,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(3154,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)],[952]) ).

thf(428,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(2032,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)],[428]) ).

thf(978,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(3207,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)],[978]) ).

thf(357,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(1883,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)],[357]) ).

thf(740,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(2705,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)],[740]) ).

thf(536,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__add__half__cancel_1) ).

thf(2264,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).

thf(603,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(2409,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)],[603]) ).

thf(148,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(1387,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)],[148]) ).

thf(364,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(1900,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)],[364]) ).

thf(129,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ 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__ineq4_0) ).

thf(1343,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ 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)],[129]) ).

thf(675,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_Transcendental_Oarctan @ A ) )
     != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__arctan__not__zero_0) ).

thf(2560,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_Transcendental_Oarctan @ A ) )
     != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).

thf(992,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(3239,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)],[992]) ).

thf(911,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(3069,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)],[911]) ).

thf(332,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(1824,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)],[332]) ).

thf(140,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(1370,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)],[140]) ).

thf(606,axiom,
    ( ( c_Transcendental_Osin @ c_Transcendental_Opi )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__pi_0) ).

thf(2414,plain,
    ( ( c_Transcendental_Osin @ c_Transcendental_Opi )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).

thf(997,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_7) ).

thf(3250,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[997]) ).

thf(474,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(2132,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)],[474]) ).

thf(826,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(2890,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)],[826]) ).

thf(1024,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(3307,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)],[1024]) ).

thf(957,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(3166,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)],[957]) ).

thf(383,axiom,
    ( ( c_Transcendental_Oarctan @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan1__eq__pi4_0) ).

thf(1938,plain,
    ( ( c_Transcendental_Oarctan @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).

thf(705,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(2628,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)],[705]) ).

thf(374,axiom,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__one__gt__zero_0) ).

thf(1920,plain,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).

thf(615,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Odiff_0) ).

thf(2433,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).

thf(975,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(3198,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)],[975]) ).

thf(61,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(1178,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)],[61]) ).

thf(818,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__eq_0) ).

thf(2872,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[818]) ).

thf(109,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__less__add__iff_1) ).

thf(1296,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).

thf(697,axiom,
    ( ( c_Transcendental_Otan @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__30_0) ).

thf(2609,plain,
    ( ( c_Transcendental_Otan @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).

thf(496,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(2179,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)],[496]) ).

thf(260,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_1) ).

thf(1656,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ F @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).

thf(512,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ c_Transcendental_Opi @ 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_sin__gt__zero__pi_0) ).

thf(2213,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ c_Transcendental_Opi @ 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)],[512]) ).

thf(150,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__divide__distrib_0) ).

thf(1392,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).

thf(369,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_9) ).

thf(1910,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).

thf(224,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Oarctan @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Oarctan @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan__minus_0) ).

thf(1573,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Oarctan @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Oarctan @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).

thf(771,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ F @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ F @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ F @ A ) @ E @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DERIV__mult__lemma_0) ).

thf(2769,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A ) @ F @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ F @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ F @ A ) @ E @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[771]) ).

thf(31,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(1106,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)],[31]) ).

thf(338,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_2) ).

thf(1837,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).

thf(236,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal )
      = ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__diff__def_0) ).

thf(1602,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal )
      = ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).

thf(719,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(2663,plain,
    class_Ring__and__Field_Oring__no__zero__divisors @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).

thf(216,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(1555,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)],[216]) ).

thf(797,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(2826,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)],[797]) ).

thf(1027,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(3314,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)],[1027]) ).

thf(446,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_5) ).

thf(2068,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).

thf(330,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(1819,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)],[330]) ).

thf(891,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(3028,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[891]) ).

thf(902,axiom,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__gt__zero_0) ).

thf(3050,plain,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[902]) ).

thf(511,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_9) ).

thf(2211,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).

thf(156,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(1407,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)],[156]) ).

thf(559,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) )
      = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__double_0) ).

thf(2313,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) )
      = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).

thf(40,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(1128,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)],[40]) ).

thf(132,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_0) ).

thf(1350,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ E @ A ) @ F @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ F @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).

thf(930,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_3) ).

thf(3105,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[930]) ).

thf(84,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(1234,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)],[84]) ).

thf(405,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_9) ).

thf(1983,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).

thf(46,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(1143,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)],[46]) ).

thf(460,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(2100,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)],[460]) ).

thf(785,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
        = B )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_3) ).

thf(2801,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ C @ A )
        = B )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[785]) ).

thf(579,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(2359,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)],[579]) ).

thf(983,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(3218,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)],[983]) ).

thf(734,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
       != ( c_HOL_Oinverse__class_Odivide @ B @ C @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__2__times__iff_1) ).

thf(2692,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
       != ( c_HOL_Oinverse__class_Odivide @ B @ C @ tc_RealDef_Oreal ) )
      | ( A
        = ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).

thf(210,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).

thf(1540,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
       != ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
      | ( C = D ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).

thf(354,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ C @ tc_RealDef_Oreal ) @ ( c_HOL_Ouminus__class_Ouminus @ D @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ouminus__class_Ouminus @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ D @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__sum__triangle__ineq_0) ).

thf(1878,plain,
    ! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ouminus__class_Ouminus @ C @ tc_RealDef_Oreal ) @ ( c_HOL_Ouminus__class_Ouminus @ D @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ouminus__class_Ouminus @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ D @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).

thf(810,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_0) ).

thf(2858,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[810]) ).

thf(937,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(3119,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)],[937]) ).

thf(915,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_2) ).

thf(3078,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( c_HOL_Oinverse__class_Odivide @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[915]) ).

thf(991,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(3237,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)],[991]) ).

thf(538,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(2268,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)],[538]) ).

thf(94,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(1259,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)],[94]) ).

thf(938,axiom,
    ( ( c_Int_OBit0 @ c_Int_OPls )
    = c_Int_OPls ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Bit0__Pls_0) ).

thf(3122,plain,
    ( ( c_Int_OBit0 @ c_Int_OPls )
    = c_Int_OPls ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[938]) ).

thf(874,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Otan @ A )
      = ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__def_0) ).

thf(2990,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Otan @ A )
      = ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[874]) ).

thf(207,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(1534,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)],[207]) ).

thf(389,axiom,
    class_OrderedGroup_Oab__group__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add) ).

thf(1953,plain,
    class_OrderedGroup_Oab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).

thf(730,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(2685,plain,
    class_Ring__and__Field_Omult__mono @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).

thf(33,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_2) ).

thf(1111,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).

thf(398,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_half__gt__zero__iff_0) ).

thf(1970,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).

thf(929,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(3102,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)],[929]) ).

thf(268,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_3) ).

thf(1672,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).

thf(709,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(2638,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)],[709]) ).

thf(36,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(1118,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)],[36]) ).

thf(962,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Osin @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__monotone__2pi_H_0) ).

thf(3176,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Osin @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[962]) ).

thf(920,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ A @ B ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ A @ C ) @ ( hAPP @ A @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Ominus__class_Ominus @ ( hAPP @ A @ C ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ A @ C ) @ ( hAPP @ A @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__MVT_0) ).

thf(3087,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ A @ B ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ A @ C ) @ ( hAPP @ A @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Ominus__class_Ominus @ ( hAPP @ A @ C ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ A @ C ) @ ( hAPP @ A @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[920]) ).

thf(886,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(3018,plain,
    class_Ring__and__Field_Ono__zero__divisors @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[886]) ).

thf(221,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(1567,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)],[221]) ).

thf(273,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(1683,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)],[273]) ).

thf(123,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(1329,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)],[123]) ).

thf(947,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(3143,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)],[947]) ).

thf(136,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(1361,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)],[136]) ).

thf(385,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_0) ).

thf(1942,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).

thf(563,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ B ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Bit0_0) ).

thf(2323,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ B ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).

thf(799,axiom,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_half_0) ).

thf(2830,plain,
    ! [A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[799]) ).

thf(163,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(1424,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)],[163]) ).

thf(451,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_5) ).

thf(2080,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).

thf(53,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(1160,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)],[53]) ).

thf(820,axiom,
    class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__normed__algebra) ).

thf(2877,plain,
    class_RealVector_Oreal__normed__algebra @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[820]) ).

thf(21,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_4) ).

thf(1082,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).

thf(424,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__add__cancel_0) ).

thf(2023,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).

thf(1033,axiom,
    ! [A: $i] :
      ( ( ( c_Transcendental_Osin @ A )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal )
        = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__zero__abs__cos__one_0) ).

thf(3326,plain,
    ! [A: $i] :
      ( ( ( c_Transcendental_Osin @ A )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal )
        = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1033]) ).

thf(924,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_5) ).

thf(3094,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[924]) ).

thf(295,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(1739,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)],[295]) ).

thf(609,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(2419,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)],[609]) ).

thf(18,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(1075,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)],[18]) ).

thf(505,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ 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_sin__gt__zero2_0) ).

thf(2196,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ 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)],[505]) ).

thf(524,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(2240,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)],[524]) ).

thf(382,axiom,
    class_Ring__and__Field_Opordered__semiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Opordered__semiring) ).

thf(1937,plain,
    class_Ring__and__Field_Opordered__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).

thf(699,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__div__pos__le_0) ).

thf(2613,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).

thf(893,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_left__distrib__number__of_0) ).

thf(3032,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[893]) ).

thf(317,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__pos_0) ).

thf(1791,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).

thf(493,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Osin @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__add_0) ).

thf(2172,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Osin @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).

thf(75,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(1214,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)],[75]) ).

thf(973,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_1) ).

thf(3194,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[973]) ).

thf(431,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__right_0) ).

thf(2038,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).

thf(172,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(1446,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)],[172]) ).

thf(359,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(1889,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)],[359]) ).

thf(254,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_2) ).

thf(1644,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).

thf(241,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(1612,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)],[241]) ).

thf(3,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(1039,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)],[3]) ).

thf(869,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(2978,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)],[869]) ).

thf(634,axiom,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__mult__self__sum__ge__zero_0) ).

thf(2472,plain,
    ! [B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).

thf(776,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_3) ).

thf(2781,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[776]) ).

thf(161,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(1419,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)],[161]) ).

thf(555,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(2304,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)],[555]) ).

thf(802,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(2836,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)],[802]) ).

thf(41,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(1131,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)],[41]) ).

thf(649,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(2505,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add__imp__le @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).

thf(677,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_2) ).

thf(2566,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).

thf(387,axiom,
    ( c_Transcendental_Opi
   != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__neq__zero_0) ).

thf(1947,plain,
    ( c_Transcendental_Opi
   != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).

thf(344,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(1852,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)],[344]) ).

thf(935,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self_0) ).

thf(3115,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[935]) ).

thf(286,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( 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_Odiff_0) ).

thf(1715,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( 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)],[286]) ).

thf(909,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_4) ).

thf(3064,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[909]) ).

thf(540,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__frac__num_0) ).

thf(2272,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).

thf(864,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_0) ).

thf(2968,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ B @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[864]) ).

thf(546,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Otan @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ B @ tc_nat ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Otan @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__periodic__nat_0) ).

thf(2285,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Otan @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ B @ tc_nat ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Otan @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).

thf(648,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add) ).

thf(2504,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).

thf(847,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(2932,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)],[847]) ).

thf(471,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
        = ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ B ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__number__of__Bit0_0) ).

thf(2125,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
        = ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ B ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).

thf(29,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(1099,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)],[29]) ).

thf(185,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(1478,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)],[185]) ).

thf(90,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(1249,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)],[90]) ).

thf(657,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ c_Transcendental_Opi @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__monotone__0__pi_0) ).

thf(2519,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ c_Transcendental_Opi @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).

thf(664,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_0) ).

thf(2536,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).

thf(728,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(2681,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)],[728]) ).

thf(641,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ B @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_1) ).

thf(2487,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ B @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).

thf(805,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_1) ).

thf(2845,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[805]) ).

thf(692,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(2598,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)],[692]) ).

thf(907,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_1) ).

thf(3059,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[907]) ).

thf(832,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(2900,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)],[832]) ).

thf(591,axiom,
    ! [A: $i] :
      ( ( ( c_Transcendental_Oarctan @ ( c_Transcendental_Otan @ A ) )
        = A )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan__tan_0) ).

thf(2387,plain,
    ! [A: $i] :
      ( ( ( c_Transcendental_Oarctan @ ( c_Transcendental_Otan @ A ) )
        = A )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).

thf(266,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(1668,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Oorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).

thf(400,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( 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__0__le__divide__iff_3) ).

thf(1974,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( 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)],[400]) ).

thf(683,axiom,
    class_Orderings_Opreorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).

thf(2581,plain,
    class_Orderings_Opreorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).

thf(12,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono__neg_0) ).

thf(1060,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ D @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).

thf(8,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(1050,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)],[8]) ).

thf(417,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ 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__square__gt__zero2_0) ).

thf(2006,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).

thf(645,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_3) ).

thf(2497,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).

thf(165,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(1429,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)],[165]) ).

thf(996,axiom,
    ! [A: $i] :
      ( c_Int_OPls
     != ( c_Int_OBit1 @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I39_J_0) ).

thf(3247,plain,
    ! [A: $i] :
      ( c_Int_OPls
     != ( c_Int_OBit1 @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[996]) ).

thf(812,axiom,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add) ).

thf(2862,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[812]) ).

thf(437,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(2052,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)],[437]) ).

thf(639,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ 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_sin__gt__zero_0) ).

thf(2482,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ 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)],[639]) ).

thf(932,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(3109,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)],[932]) ).

thf(403,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_9) ).

thf(1979,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).

thf(913,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(3074,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)],[913]) ).

thf(917,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(3083,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)],[917]) ).

thf(976,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(3201,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)],[976]) ).

thf(303,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_3) ).

thf(1759,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).

thf(583,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(2370,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)],[583]) ).

thf(982,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(3215,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)],[982]) ).

thf(844,axiom,
    ! [A: $i] :
      ( ( ( c_Transcendental_Ocos @ 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_Otimes__class_Otimes @ ( c_RealDef_Oreal @ ( c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1 @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__zero__lemma_1) ).

thf(2926,plain,
    ! [A: $i] :
      ( ( ( c_Transcendental_Ocos @ 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_Otimes__class_Otimes @ ( c_RealDef_Oreal @ ( c_Transcendental_Osko__Transcendental__Xcos__zero__lemma__1__1 @ A ) @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[844]) ).

thf(23,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(1086,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)],[23]) ).

thf(668,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ 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_cos__gt__zero_0) ).

thf(2546,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ 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)],[668]) ).

thf(312,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(1779,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)],[312]) ).

thf(1011,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(3279,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)],[1011]) ).

thf(439,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__sin__le__one_0) ).

thf(2057,plain,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).

thf(618,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Osin @ 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 )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__less__zero_0) ).

thf(2440,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Osin @ 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 )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).

thf(199,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Oarctan @ A ) @ ( c_Transcendental_Oarctan @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan__monotone_0) ).

thf(1515,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Oarctan @ A ) @ ( c_Transcendental_Oarctan @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).

thf(362,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(1895,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)],[362]) ).

thf(292,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_2) ).

thf(1732,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).

thf(167,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__le__0__iff_1) ).

thf(1434,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).

thf(346,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Otan @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Otan @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__minus_0) ).

thf(1857,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Otan @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Otan @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).

thf(409,axiom,
    ~ ( c_HOL_Oord__class_Oless @ c_Transcendental_Opi @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__not__less__zero_0) ).

thf(1991,plain,
    ~ ( c_HOL_Oord__class_Oless @ c_Transcendental_Opi @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).

thf(779,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(2788,plain,
    class_OrderedGroup_Olordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[779]) ).

thf(119,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(1318,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)],[119]) ).

thf(71,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(1202,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)],[71]) ).

thf(508,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(2203,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)],[508]) ).

thf(823,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_8) ).

thf(2883,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[823]) ).

thf(960,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__cos__squared__add3_0) ).

thf(3173,plain,
    ! [A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[960]) ).

thf(762,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_7) ).

thf(2748,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[762]) ).

thf(58,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(1170,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)],[58]) ).

thf(862,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A )
        = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__imp_0) ).

thf(2963,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A )
        = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[862]) ).

thf(1031,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(3321,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)],[1031]) ).

thf(1,negated_conjecture,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ v_n @ tc_nat ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).

thf(1035,plain,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ v_n @ tc_nat ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).

thf(180,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(1466,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)],[180]) ).

thf(599,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Osin @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__periodic_0) ).

thf(2402,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Osin @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).

thf(455,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_1) ).

thf(2089,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).

thf(971,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( B
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_0) ).

thf(3190,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( B
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[971]) ).

thf(502,axiom,
    ! [A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal )
      = ( c_Transcendental_Ocos @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__sin__cos__eq_0) ).

thf(2189,plain,
    ! [A: $i] :
      ( ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal )
      = ( c_Transcendental_Ocos @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).

thf(876,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_7) ).

thf(2995,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[876]) ).

thf(570,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(2338,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)],[570]) ).

thf(412,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Oplus__class_Oplus @ c_Transcendental_Opi @ 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__periodic__pi2_0) ).

thf(1996,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Oplus__class_Oplus @ c_Transcendental_Opi @ A @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).

thf(611,axiom,
    ! [A: $i] :
      ( ( ( c_Int_OBit0 @ A )
       != c_Int_OPls )
      | ( A = c_Int_OPls ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I44_J_0) ).

thf(2423,plain,
    ! [A: $i] :
      ( ( ( c_Int_OBit0 @ A )
       != c_Int_OPls )
      | ( A = c_Int_OPls ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).

thf(661,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(2529,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)],[661]) ).

thf(480,axiom,
    ( c_Int_OPls
    = ( c_Int_OBit0 @ c_Int_OPls ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I38_J_1) ).

thf(2144,plain,
    ( c_Int_OPls
    = ( c_Int_OBit0 @ c_Int_OPls ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).

thf(102,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(1278,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)],[102]) ).

thf(256,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_1) ).

thf(1648,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).

thf(415,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(2001,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)],[415]) ).

thf(605,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(2413,plain,
    class_Ring__and__Field_Opordered__ring__abs @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).

thf(550,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(2292,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)],[550]) ).

thf(1000,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Oab__semigroup__mult) ).

thf(3257,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1000]) ).

thf(100,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(1273,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)],[100]) ).

thf(933,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Oplus__class_Oplus @ A @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__periodic__pi_0) ).

thf(3111,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Oplus__class_Oplus @ A @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[933]) ).

thf(248,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ E @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__le_0) ).

thf(1631,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ E @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).

thf(534,axiom,
    ( ( c_Transcendental_Otan @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__zero_0) ).

thf(2260,plain,
    ( ( c_Transcendental_Otan @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).

thf(290,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_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_1) ).

thf(1727,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_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).

thf(197,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_0) ).

thf(1510,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).

thf(393,axiom,
    class_Ring__and__Field_Oidom @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oidom) ).

thf(1959,plain,
    class_Ring__and__Field_Oidom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).

thf(673,axiom,
    ! [A: $i] :
      ( ( ( c_Transcendental_Otan @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ) @ ( c_HOL_Oplus__class_Oplus @ ( c_Transcendental_Ocos @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__half_0) ).

thf(2556,plain,
    ! [A: $i] :
      ( ( ( c_Transcendental_Otan @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ) @ ( c_HOL_Oplus__class_Oplus @ ( c_Transcendental_Ocos @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).

thf(531,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_9) ).

thf(2253,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).

thf(541,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__numeral__0__right_0) ).

thf(2275,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).

thf(483,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_9) ).

thf(2149,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).

thf(213,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__iff__diff__less__0_0) ).

thf(1548,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).

thf(378,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(1927,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)],[378]) ).

thf(111,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(1301,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)],[111]) ).

thf(753,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(2734,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)],[753]) ).

thf(828,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Osko__Transcendental__Xtan__total__pi4__1__1 @ A ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__total__pi4_1) ).

thf(2894,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Osko__Transcendental__Xtan__total__pi4__1__1 @ A ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[828]) ).

thf(142,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(1374,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)],[142]) ).

thf(51,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(1154,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)],[51]) ).

thf(969,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_5) ).

thf(3187,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[969]) ).

thf(750,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
        = ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__div__pos_0) ).

thf(2727,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ C @ A )
        = ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).

thf(435,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(2048,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)],[435]) ).

thf(517,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_6) ).

thf(2225,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).

thf(919,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(3086,plain,
    class_OrderedGroup_Ocancel__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[919]) ).

thf(787,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__le__interval__iff_1) ).

thf(2806,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[787]) ).

thf(154,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonneg__neg_0) ).

thf(1403,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).

thf(745,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Transcendental_Otan @ A ) @ tc_RealDef_Oreal )
      = ( c_Transcendental_Otan @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__inverse_0) ).

thf(2716,plain,
    ! [A: $i] :
      ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Transcendental_Otan @ A ) @ tc_RealDef_Oreal )
      = ( c_Transcendental_Otan @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).

thf(396,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_7) ).

thf(1965,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).

thf(201,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(1520,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)],[201]) ).

thf(475,axiom,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__two__pi_0) ).

thf(2134,plain,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).

thf(865,axiom,
    class_Ring__and__Field_Oring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Oring) ).

thf(2970,plain,
    class_Ring__and__Field_Oring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[865]) ).

thf(1030,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__add__half__cancel_0) ).

thf(3319,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ A @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1030]) ).

thf(314,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(1784,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)],[314]) ).

thf(999,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__average__minus__first_0) ).

thf(3255,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ A @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[999]) ).

thf(780,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(2789,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)],[780]) ).

thf(39,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).

thf(1125,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_lessequals @ E @ D @ A )
      | ~ ( c_lessequals @ C @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).

thf(501,axiom,
    class_Ring__and__Field_Ocomm__semiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Ocomm__semiring) ).

thf(2188,plain,
    class_Ring__and__Field_Ocomm__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).

thf(870,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(2981,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)],[870]) ).

thf(244,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
       != ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A )
        = F ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_0) ).

thf(1620,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
       != ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A )
        = F ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).

thf(642,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(2489,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)],[642]) ).

thf(258,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(1652,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)],[258]) ).

thf(916,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_6) ).

thf(3081,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[916]) ).

thf(379,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__neg__neg_0) ).

thf(1929,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).

thf(1004,axiom,
    c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__less__two_0) ).

thf(3266,plain,
    c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1004]) ).

thf(724,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(2674,plain,
    class_OrderedGroup_Opordered__ab__group__add__abs @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).

thf(421,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ c_Transcendental_Opi @ ( c_RealDef_Oreal @ A @ tc_nat ) @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__npi2_0) ).

thf(2016,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ c_Transcendental_Opi @ ( c_RealDef_Oreal @ A @ tc_nat ) @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).

thf(654,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(2514,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)],[654]) ).

thf(678,axiom,
    ! [A: $i] :
      ( ( ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal )
        = ( c_HOL_Ouminus__class_Ouminus @ A @ 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__abs__def_0) ).

thf(2568,plain,
    ! [A: $i] :
      ( ( ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal )
        = ( c_HOL_Ouminus__class_Ouminus @ A @ 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)],[678]) ).

thf(319,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__divide__distrib_0) ).

thf(1795,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).

thf(280,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__triangle__ineq_0) ).

thf(1701,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ D @ E @ A ) @ A ) @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).

thf(596,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(2398,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)],[596]) ).

thf(81,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(1226,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)],[81]) ).

thf(735,axiom,
    c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__two__ge__zero_0) ).

thf(2695,plain,
    c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).

thf(93,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(1256,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)],[93]) ).

thf(860,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_4) ).

thf(2959,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[860]) ).

thf(981,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_4) ).

thf(3213,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[981]) ).

thf(985,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ D @ A ) )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__num__frac_0) ).

thf(3223,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A ) @ D @ A ) )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[985]) ).

thf(44,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(1139,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)],[44]) ).

thf(564,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Otan @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Otan @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__periodic_0) ).

thf(2326,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Otan @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Otan @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).

thf(903,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(3051,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)],[903]) ).

thf(99,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__nonpos__pos_0) ).

thf(1271,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).

thf(116,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(1312,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)],[116]) ).

thf(11,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(1058,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)],[11]) ).

thf(86,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(1239,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)],[86]) ).

thf(306,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(1765,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)],[306]) ).

thf(363,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_group__add__class_Odiff__0_0) ).

thf(1897,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).

thf(80,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(1224,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)],[80]) ).

thf(680,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
       != ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of_1) ).

thf(2573,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
       != ( c_Int_Onumber__class_Onumber__of @ C @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).

thf(889,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
       != ( 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__sum__squares__cancel_0) ).

thf(3023,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
       != ( 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)],[889]) ).

thf(504,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Oadd_0) ).

thf(2193,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).

thf(315,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(1786,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)],[315]) ).

thf(936,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(3118,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[936]) ).

thf(515,axiom,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__30_0) ).

thf(2220,plain,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).

thf(250,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(1635,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)],[250]) ).

thf(879,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(3002,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)],[879]) ).

thf(619,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_7) ).

thf(2442,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).

thf(764,axiom,
    class_Int_Onumber__ring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Int_Onumber__ring) ).

thf(2753,plain,
    class_Int_Onumber__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[764]) ).

thf(922,axiom,
    class_Ring__and__Field_Oordered__semiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Oordered__semiring) ).

thf(3091,plain,
    class_Ring__and__Field_Oordered__semiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[922]) ).

thf(179,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(1464,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)],[179]) ).

thf(652,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_5) ).

thf(2510,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).

thf(573,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_8) ).

thf(2346,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).

thf(580,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(2361,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)],[580]) ).

thf(747,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(2721,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)],[747]) ).

thf(665,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(2538,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)],[665]) ).

thf(453,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__minus__divide__right_0) ).

thf(2084,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).

thf(872,axiom,
    class_Ring__and__Field_Ofield @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Ofield) ).

thf(2987,plain,
    class_Ring__and__Field_Ofield @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[872]) ).

thf(7,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_0) ).

thf(1048,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).

thf(722,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
        = B )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_0) ).

thf(2669,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
        = B )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).

thf(928,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(3101,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)],[928]) ).

thf(658,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(2521,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)],[658]) ).

thf(104,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_0) ).

thf(1282,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).

thf(637,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_6) ).

thf(2478,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).

thf(484,axiom,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ A @ tc_nat ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__ge__zero_0) ).

thf(2151,plain,
    ! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ A @ tc_nat ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).

thf(519,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( B
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_0) ).

thf(2229,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( B
        = ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).

thf(773,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(2774,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)],[773]) ).

thf(1014,axiom,
    ! [A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_numeral__1__eq__1_0) ).

thf(3287,plain,
    ! [A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A )
        = ( c_HOL_Oone__class_Oone @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1014]) ).

thf(203,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_5) ).

thf(1524,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).

thf(459,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(2097,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)],[459]) ).

thf(1007,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( B
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of1_3) ).

thf(3270,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( B
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1007]) ).

thf(533,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(2257,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)],[533]) ).

thf(230,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(1589,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)],[230]) ).

thf(527,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(2246,plain,
    class_Ring__and__Field_Ocomm__semiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).

thf(190,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(1492,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)],[190]) ).

thf(553,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Oplus__class_Oplus @ A @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__periodic__pi_0) ).

thf(2299,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Oplus__class_Oplus @ A @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).

thf(467,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(2116,plain,
    class_Ring__and__Field_Olordered__ring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).

thf(803,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__frac__eq_0) ).

thf(2839,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ E @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ E @ A ) @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[803]) ).

thf(309,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(1771,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)],[309]) ).

thf(852,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_5) ).

thf(2943,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[852]) ).

thf(853,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(2945,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)],[853]) ).

thf(586,axiom,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__two__gt__zero_0) ).

thf(2378,plain,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).

thf(965,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Osin @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__diff_0) ).

thf(3182,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Osin @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[965]) ).

thf(829,axiom,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Opordered__comm__monoid__add) ).

thf(2896,plain,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[829]) ).

thf(223,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(1571,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)],[223]) ).

thf(169,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_5) ).

thf(1439,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).

thf(444,axiom,
    ( ( c_Transcendental_Otan @ c_Transcendental_Opi )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__pi_0) ).

thf(2065,plain,
    ( ( c_Transcendental_Otan @ c_Transcendental_Opi )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).

thf(60,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ocancel__semigroup__add @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ B @ C @ A )
       != ( c_HOL_Oplus__class_Oplus @ B @ D @ A ) )
      | ( C = D ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__left__cancel_0) ).

thf(1175,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)],[60]) ).

thf(796,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__div__pos__less_0) ).

thf(2824,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[796]) ).

thf(497,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(2182,plain,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).

thf(182,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(1471,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)],[182]) ).

thf(758,axiom,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocancel__semigroup__add) ).

thf(2742,plain,
    class_OrderedGroup_Ocancel__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[758]) ).

thf(695,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ A )
      = ( c_Transcendental_Ocos @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__cos__eq_0) ).

thf(2605,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ A )
      = ( c_Transcendental_Ocos @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).

thf(465,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_4) ).

thf(2111,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).

thf(410,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(1993,plain,
    class_Ring__and__Field_Oordered__comm__semiring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).

thf(348,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(1862,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)],[348]) ).

thf(177,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(1460,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)],[177]) ).

thf(720,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(2664,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)],[720]) ).

thf(145,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Otan @ ( c_Transcendental_Oarctan @ A ) )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan_2) ).

thf(1381,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Otan @ ( c_Transcendental_Oarctan @ A ) )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).

thf(275,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus_0) ).

thf(1688,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).

thf(425,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Otan @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ 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_tan__gt__zero_0) ).

thf(2025,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Otan @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ 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)],[425]) ).

thf(790,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(2812,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)],[790]) ).

thf(20,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(1080,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)],[20]) ).

thf(943,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_3) ).

thf(3133,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[943]) ).

thf(905,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(3055,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)],[905]) ).

thf(217,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(1557,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)],[217]) ).

thf(572,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 ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ 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_sin__cos__between__zero__two__pi_0) ).

thf(2343,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 ) )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ 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)],[572]) ).

thf(704,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__imp_0) ).

thf(2625,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ C @ B @ A ) @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).

thf(368,axiom,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oarctan @ A ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan_0) ).

thf(1909,plain,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oarctan @ A ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).

thf(54,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_3) ).

thf(1162,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).

thf(621,axiom,
    class_Ring__and__Field_Omult__mono @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Omult__mono) ).

thf(2446,plain,
    class_Ring__and__Field_Omult__mono @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).

thf(766,axiom,
    ! [A: $i] :
      ( ( c_Int_OPls
       != ( c_Int_OBit0 @ A ) )
      | ( c_Int_OPls = A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I38_J_0) ).

thf(2757,plain,
    ! [A: $i] :
      ( ( c_Int_OPls
       != ( c_Int_OBit0 @ A ) )
      | ( c_Int_OPls = A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[766]) ).

thf(690,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(2593,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)],[690]) ).

thf(881,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(3006,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)],[881]) ).

thf(49,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(1149,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)],[49]) ).

thf(1019,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(3298,plain,
    class_Ring__and__Field_Oordered__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1019]) ).

thf(108,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ C @ A ) @ E @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_1) ).

thf(1293,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ D @ B @ A ) @ C @ A ) @ E @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ E @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).

thf(542,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ A @ tc_nat ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__2npi_0) ).

thf(2278,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ A @ tc_nat ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).

thf(671,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(2553,plain,
    class_Ring__and__Field_Ocomm__semiring__1 @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).

thf(629,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(2461,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)],[629]) ).

thf(867,axiom,
    c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__ge__zero_0) ).

thf(2974,plain,
    c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[867]) ).

thf(804,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(2842,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)],[804]) ).

thf(950,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_4) ).

thf(3150,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[950]) ).

thf(566,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_0) ).

thf(2329,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).

thf(742,axiom,
    class_OrderedGroup_Oab__semigroup__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult) ).

thf(2710,plain,
    class_OrderedGroup_Oab__semigroup__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).

thf(836,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(2911,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)],[836]) ).

thf(449,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(2075,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)],[449]) ).

thf(575,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(2350,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)],[575]) ).

thf(477,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(2139,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)],[477]) ).

thf(846,axiom,
    class_Orderings_Olinorder @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).

thf(2931,plain,
    class_Orderings_Olinorder @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[846]) ).

thf(526,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(2244,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)],[526]) ).

thf(192,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(1496,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)],[192]) ).

thf(878,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A )
        = C )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_0) ).

thf(2999,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A )
        = C )
      | ( D
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[878]) ).

thf(815,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_1) ).

thf(2867,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[815]) ).

thf(650,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__pos__pos_0) ).

thf(2506,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).

thf(69,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__less__0__iff_0) ).

thf(1198,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ B @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).

thf(340,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(1841,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)],[340]) ).

thf(749,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_9) ).

thf(2725,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).

thf(598,axiom,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult) ).

thf(2401,plain,
    class_OrderedGroup_Ocomm__monoid__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).

thf(279,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_2) ).

thf(1699,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).

thf(769,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(2765,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)],[769]) ).

thf(5,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(1044,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)],[5]) ).

thf(670,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__2__right_0) ).

thf(2550,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).

thf(88,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(1245,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)],[88]) ).

thf(954,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(3159,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)],[954]) ).

thf(443,axiom,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__refl_0) ).

thf(2064,plain,
    ! [A: $i] : ( c_lessequals @ A @ A @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).

thf(993,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ 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_divide__less__0__1__iff_1) ).

thf(3241,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ 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)],[993]) ).

thf(34,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__minus__eq__add_0) ).

thf(1113,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).

thf(783,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(2797,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)],[783]) ).

thf(885,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(3016,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)],[885]) ).

thf(707,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
       != ( c_HOL_Oone__class_Oone @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__inverse__eq_0) ).

thf(2633,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
       != ( c_HOL_Oone__class_Oone @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).

thf(1025,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(3310,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)],[1025]) ).

thf(137,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__number__of__eq__not__less_1) ).

thf(1364,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Orderings_Olinorder @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).

thf(592,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ 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__divide__1__iff_1) ).

thf(2390,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).

thf(963,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(3178,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)],[963]) ).

thf(30,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(1102,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)],[30]) ).

thf(871,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(2984,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)],[871]) ).

thf(323,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ C @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__left__mono_0) ).

thf(1805,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ A @ C @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ C @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).

thf(159,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( 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_Odiff_0) ).

thf(1413,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( 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)],[159]) ).

thf(438,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq__number__of_4) ).

thf(2054,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_Int_Onumber__class_Onumber__of @ B @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).

thf(523,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(2239,plain,
    class_Ring__and__Field_Oordered__ring__strict @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).

thf(325,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_2) ).

thf(1809,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).

thf(263,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff1_0) ).

thf(1662,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).

thf(73,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(1208,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)],[73]) ).

thf(1016,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(3293,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)],[1016]) ).

thf(821,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(2878,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)],[821]) ).

thf(521,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(2234,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)],[521]) ).

thf(624,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ A @ tc_nat ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__npi_0) ).

thf(2449,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ A @ tc_nat ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).

thf(901,axiom,
    ! [A: $i] :
      ( ( c_FFT__Mirabelle_Oroot @ A )
      = ( c_Complex_Ocis @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ A @ tc_nat ) @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_FFT__Mirabelle_Oroot__def_0) ).

thf(3048,plain,
    ! [A: $i] :
      ( ( c_FFT__Mirabelle_Oroot @ A )
      = ( c_Complex_Ocis @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ A @ tc_nat ) @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[901]) ).

thf(128,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(1340,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)],[128]) ).

thf(47,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(1145,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)],[47]) ).

thf(62,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(1181,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)],[62]) ).

thf(684,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ A @ tc_nat ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__2npi_0) ).

thf(2582,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Ocos @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ ( c_RealDef_Oreal @ A @ tc_nat ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).

thf(246,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(1626,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)],[246]) ).

thf(882,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Transcendental_Otan @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ B )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ A )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__add_0) ).

thf(3009,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Transcendental_Otan @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ B )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ A )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[882]) ).

thf(838,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(2914,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)],[838]) ).

thf(792,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(2816,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)],[792]) ).

thf(228,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__0__right_0) ).

thf(1583,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).

thf(112,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(1304,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Orderings_Opreorder @ A )
      | ( c_lessequals @ B @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).

thf(352,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__triangle__ineq3_0) ).

thf(1873,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( c_lessequals @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) @ A ) @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).

thf(972,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(3193,plain,
    class_OrderedGroup_Oordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[972]) ).

thf(56,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(1166,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)],[56]) ).

thf(463,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(2107,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)],[463]) ).

thf(561,axiom,
    ! [A: $i] :
      ( ( c_NthRoot_Osqrt @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) )
      = ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__abs2_0) ).

thf(2318,plain,
    ! [A: $i] :
      ( ( c_NthRoot_Osqrt @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) )
      = ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).

thf(777,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_7) ).

thf(2784,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[777]) ).

thf(955,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(3161,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)],[955]) ).

thf(366,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_1) ).

thf(1905,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).

thf(851,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(2942,plain,
    class_Ring__and__Field_Oabs__if @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[851]) ).

thf(299,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(1748,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)],[299]) ).

thf(320,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(1798,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)],[320]) ).

thf(595,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(2397,plain,
    class_Ring__and__Field_Omult__mono1 @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).

thf(16,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(1070,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)],[16]) ).

thf(718,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osko__Transcendental__Xtan__total__pi4__1__1 @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__total__pi4_0) ).

thf(2661,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osko__Transcendental__Xtan__total__pi4__1__1 @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).

thf(479,axiom,
    class_Orderings_Oorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Oorder) ).

thf(2143,plain,
    class_Orderings_Oorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).

thf(1002,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(3260,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)],[1002]) ).

thf(91,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
      | ~ ( c_lessequals @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__add__iff2_1) ).

thf(1252,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_lessequals @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) @ A )
      | ~ ( c_lessequals @ D @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).

thf(139,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(1368,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)],[139]) ).

thf(206,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(1531,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)],[206]) ).

thf(813,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__minus__iff_0) ).

thf(2863,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[813]) ).

thf(234,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(1598,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)],[234]) ).

thf(585,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(2375,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)],[585]) ).

thf(52,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(1156,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_NthRoot_Osqrt @ A )
       != ( c_NthRoot_Osqrt @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).

thf(441,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__left__mono_0) ).

thf(2060,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).

thf(297,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__diff__cancel_0) ).

thf(1743,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ C @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).

thf(726,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(2678,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)],[726]) ).

thf(656,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(2518,plain,
    class_OrderedGroup_Opordered__comm__monoid__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).

thf(794,axiom,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ c_Transcendental_Opi @ 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_sin__ge__zero_0) ).

thf(2821,plain,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ c_Transcendental_Opi @ 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)],[794]) ).

thf(979,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nonzero__abs__divide_0) ).

thf(3209,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oabs__class_Oabs @ B @ A ) @ ( c_HOL_Oabs__class_Oabs @ C @ A ) @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[979]) ).

thf(301,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).

thf(1753,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
      | ( c_HOL_Oord__class_Oless @ B @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).

thf(602,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_6) ).

thf(2407,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).

thf(97,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ E @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less2_0) ).

thf(1267,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ E @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
      | ~ ( c_lessequals @ B @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).

thf(807,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__Numeral1_0) ).

thf(2850,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[807]) ).

thf(187,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(1484,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)],[187]) ).

thf(488,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Ocos @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ 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_cos__double__less__one_0) ).

thf(2160,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Ocos @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ 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)],[488]) ).

thf(841,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(2920,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)],[841]) ).

thf(95,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(1262,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)],[95]) ).

thf(472,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_0) ).

thf(2128,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).

thf(261,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__iff_2) ).

thf(1658,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).

thf(271,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(1679,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)],[271]) ).

thf(1034,axiom,
    ! [A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oone__class_Oone @ A )
        = ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__arith_I110_J_0) ).

thf(3329,plain,
    ! [A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oone__class_Oone @ A )
        = ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1034]) ).

thf(577,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_5) ).

thf(2354,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).

thf(716,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(2656,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)],[716]) ).

thf(284,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(1711,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)],[284]) ).

thf(887,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(3019,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)],[887]) ).

thf(761,axiom,
    class_RealVector_Oreal__field @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__RealVector_Oreal__field) ).

thf(2747,plain,
    class_RealVector_Oreal__field @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[761]) ).

thf(9,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(1053,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)],[9]) ).

thf(193,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ E @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__less_0) ).

thf(1499,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) @ A )
      | ~ ( c_lessequals @ E @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ E @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).

thf(407,axiom,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Oarctan @ A ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan_1) ).

thf(1987,plain,
    ! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Oarctan @ A ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).

thf(626,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(2454,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)],[626]) ).

thf(1023,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_0) ).

thf(3305,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1023]) ).

thf(166,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__gt__zero__less_0) ).

thf(1432,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).

thf(327,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(1813,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)],[327]) ).

thf(174,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(1452,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)],[174]) ).

thf(251,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(1637,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)],[251]) ).

thf(732,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(2688,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)],[732]) ).

thf(1008,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_4) ).

thf(3273,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1008]) ).

thf(65,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(1188,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)],[65]) ).

thf(64,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_3) ).

thf(1186,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).

thf(890,axiom,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__add__one__not__less__self_0) ).

thf(3026,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[890]) ).

thf(613,axiom,
    c_HOL_Oord__class_Oless @ ( c_Transcendental_Ocos @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__two__less__zero_0) ).

thf(2429,plain,
    c_HOL_Oord__class_Oless @ ( c_Transcendental_Ocos @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).

thf(335,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__diff__less__iff_1) ).

thf(1830,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).

thf(305,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_3) ).

thf(1763,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).

thf(940,axiom,
    c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__half__le__two_0) ).

thf(3127,plain,
    c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[940]) ).

thf(209,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transcendental_Oarctan @ A ) @ ( c_Transcendental_Oarctan @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan__monotone_H_0) ).

thf(1538,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transcendental_Oarctan @ A ) @ ( c_Transcendental_Oarctan @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).

thf(738,axiom,
    ( ( c_Transcendental_Otan @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__45_0) ).

thf(2701,plain,
    ( ( c_Transcendental_Otan @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).

thf(77,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(1218,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)],[77]) ).

thf(897,axiom,
    ( ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
    = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oarctan @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oarctan @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_machin_0) ).

thf(3041,plain,
    ( ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
    = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oarctan @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal ) @ ( c_Transcendental_Oarctan @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) ) ) ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[897]) ).

thf(632,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(2468,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)],[632]) ).

thf(78,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__iff_0) ).

thf(1220,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).

thf(381,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_2) ).

thf(1934,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ozero__class_Ozero @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).

thf(604,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Otan @ 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 )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__less__zero_0) ).

thf(2411,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Otan @ 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 )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).

thf(343,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_0) ).

thf(1849,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).

thf(466,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(2113,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)],[466]) ).

thf(322,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(1802,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)],[322]) ).

thf(587,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ c_Transcendental_Opi @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ A @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__monotone__0__pi_H_0) ).

thf(2379,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ c_Transcendental_Opi @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ A @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).

thf(391,axiom,
    ! [B: $i,A: $i] :
      ( ( c_NthRoot_Osqrt @ ( c_HOL_Oinverse__class_Odivide @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Oinverse__class_Odivide @ ( c_NthRoot_Osqrt @ A ) @ ( c_NthRoot_Osqrt @ B ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__divide_0) ).

thf(1955,plain,
    ! [B: $i,A: $i] :
      ( ( c_NthRoot_Osqrt @ ( c_HOL_Oinverse__class_Odivide @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Oinverse__class_Odivide @ ( c_NthRoot_Osqrt @ A ) @ ( c_NthRoot_Osqrt @ B ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).

thf(682,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_5) ).

thf(2579,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).

thf(164,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_3) ).

thf(1427,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).

thf(195,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(1504,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)],[195]) ).

thf(267,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__divide__iff_0) ).

thf(1670,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).

thf(427,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = A ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sum__of__halves_0) ).

thf(2030,plain,
    ! [A: $i] :
      ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ A @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      = A ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).

thf(850,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
       != ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ E @ A )
        = ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_0) ).

thf(2939,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ C @ A )
       != ( c_HOL_Oinverse__class_Odivide @ D @ E @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ E @ A )
        = ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[850]) ).

thf(912,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(3071,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)],[912]) ).

thf(356,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(1881,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)],[356]) ).

thf(537,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Otan @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ A @ tc_nat ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__npi_0) ).

thf(2266,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Otan @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ A @ tc_nat ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).

thf(685,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(2584,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)],[685]) ).

thf(243,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(1617,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)],[243]) ).

thf(725,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(2675,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)],[725]) ).

thf(135,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(1358,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)],[135]) ).

thf(528,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_0) ).

thf(2247,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).

thf(211,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(1543,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)],[211]) ).

thf(931,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_9) ).

thf(3107,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[931]) ).

thf(45,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_3) ).

thf(1141,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).

thf(939,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__self__if_1) ).

thf(3124,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ B @ A )
        = ( c_HOL_Oone__class_Oone @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[939]) ).

thf(612,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(2426,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)],[612]) ).

thf(875,axiom,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
      | ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ A @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__zero__iff_4) ).

thf(2992,plain,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
      | ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ A @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[875]) ).

thf(208,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(1536,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)],[208]) ).

thf(404,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_9) ).

thf(1981,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).

thf(105,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(1284,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)],[105]) ).

thf(868,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
       != ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ E @ A )
        = ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_frac__eq__eq_1) ).

thf(2975,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ B @ C @ A )
       != ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( E
        = ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ E @ A )
        = ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[868]) ).

thf(399,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_1) ).

thf(1972,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).

thf(562,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(2320,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)],[562]) ).

thf(743,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
        = B )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq__number__of1_3) ).

thf(2711,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
        = B )
      | ( ( c_Int_Onumber__class_Onumber__of @ C @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).

thf(811,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(2860,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)],[811]) ).

thf(855,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(2949,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)],[855]) ).

thf(141,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(1372,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)],[141]) ).

thf(827,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__right__mono_0) ).

thf(2892,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[827]) ).

thf(339,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(1839,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)],[339]) ).

thf(910,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(3067,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)],[910]) ).

thf(824,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq_7) ).

thf(2885,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[824]) ).

thf(259,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(1654,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)],[259]) ).

thf(698,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_1) ).

thf(2611,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).

thf(711,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(2643,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)],[711]) ).

thf(717,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(2658,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)],[717]) ).

thf(413,axiom,
    class_Ring__and__Field_Osemiring @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Ring__and__Field_Osemiring) ).

thf(1998,plain,
    class_Ring__and__Field_Osemiring @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).

thf(819,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(2875,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)],[819]) ).

thf(958,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero__left_0) ).

thf(3168,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[958]) ).

thf(384,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(1940,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)],[384]) ).

thf(1013,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__divide__mult__cancel__left_0) ).

thf(3284,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) )
      | ( B
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1013]) ).

thf(767,axiom,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ ( c_RealDef_Oreal @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__real__of__nat__less__zero_0) ).

thf(2760,plain,
    ! [A: $i] :
      ~ ( c_HOL_Oord__class_Oless @ ( c_RealDef_Oreal @ A @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[767]) ).

thf(162,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(1421,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)],[162]) ).

thf(420,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(2013,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)],[420]) ).

thf(843,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(2924,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)],[843]) ).

thf(373,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Otan @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Otan @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__periodic__n_0) ).

thf(1918,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Otan @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      = ( c_Transcendental_Otan @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).

thf(118,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_3) ).

thf(1316,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).

thf(22,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(1084,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)],[22]) ).

thf(433,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(2045,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)],[433]) ).

thf(923,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(3092,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)],[923]) ).

thf(736,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_4) ).

thf(2696,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).

thf(215,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(1553,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)],[215]) ).

thf(817,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_9) ).

thf(2870,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[817]) ).

thf(798,axiom,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__gt__zero__pi_0) ).

thf(2828,plain,
    ! [A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[798]) ).

thf(329,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(1817,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)],[329]) ).

thf(959,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_1) ).

thf(3171,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[959]) ).

thf(450,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__imp__less__div__pos_0) ).

thf(2078,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).

thf(120,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_3) ).

thf(1321,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).

thf(337,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(1834,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)],[337]) ).

thf(558,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(2310,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)],[558]) ).

thf(341,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_class__ringb_Osubr0__iff_1) ).

thf(1844,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oidom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).

thf(513,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(2215,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)],[513]) ).

thf(200,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(1517,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)],[200]) ).

thf(76,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(1216,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)],[76]) ).

thf(510,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_4) ).

thf(2209,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).

thf(759,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(2743,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)],[759]) ).

thf(877,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__1__iff_0) ).

thf(2997,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[877]) ).

thf(500,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(2187,plain,
    class_Ring__and__Field_Oordered__idom @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).

thf(464,axiom,
    c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__ge__two_0) ).

thf(2110,plain,
    c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).

thf(149,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__half__sum_0) ).

thf(1390,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).

thf(225,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ E @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult_Oprod__diff__prod_0) ).

thf(1575,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ E @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ E @ A ) @ A ) @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_HOL_Ominus__class_Ominus @ C @ E @ A ) @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).

thf(293,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(1734,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)],[293]) ).

thf(781,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_5) ).

thf(2792,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[781]) ).

thf(324,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(1807,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)],[324]) ).

thf(32,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(1108,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)],[32]) ).

thf(896,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(3039,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)],[896]) ).

thf(101,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__le__divide__iff_1) ).

thf(1276,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).

thf(255,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(1646,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)],[255]) ).

thf(122,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(1326,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)],[122]) ).

thf(741,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(2707,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)],[741]) ).

thf(491,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__zero_0) ).

thf(2167,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).

thf(672,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_4) ).

thf(2554,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).

thf(13,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(1062,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)],[13]) ).

thf(186,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(1481,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)],[186]) ).

thf(795,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(2823,plain,
    class_OrderedGroup_Olordered__ab__group__add__abs @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[795]) ).

thf(866,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Int_OBit0 @ A )
     != ( c_Int_OBit1 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I49_J_0) ).

thf(2971,plain,
    ! [B: $i,A: $i] :
      ( ( c_Int_OBit0 @ A )
     != ( c_Int_OBit1 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[866]) ).

thf(990,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(3235,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)],[990]) ).

thf(331,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(1822,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)],[331]) ).

thf(473,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_6) ).

thf(2130,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).

thf(945,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Int_OBit0 @ A )
       != ( c_Int_OBit0 @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I48_J_0) ).

thf(3136,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Int_OBit0 @ A )
       != ( c_Int_OBit0 @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[945]) ).

thf(998,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(3252,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)],[998]) ).

thf(918,axiom,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__add) ).

thf(3085,plain,
    class_OrderedGroup_Omonoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[918]) ).

thf(873,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ B @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__le__divide__iff_0) ).

thf(2988,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ B @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[873]) ).

thf(147,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__add__iff1_0) ).

thf(1385,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Opordered__ring @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A ) @ E @ A ) @ F @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ E @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ F @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).

thf(288,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__minus__eq_0) ).

thf(1721,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Ogroup__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).

thf(494,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( B
        = ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__eq__0__iff_0) ).

thf(2174,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal )
       != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( B
        = ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).

thf(545,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of1_2) ).

thf(2283,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).

thf(184,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__right__mono_0) ).

thf(1476,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ B @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).

thf(269,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(1674,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)],[269]) ).

thf(809,axiom,
    ! [A: $i] :
      ( ( ( c_Transcendental_Otan @ ( c_Transcendental_Osko__Transcendental__Xtan__total__pi4__1__1 @ A ) )
        = A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__total__pi4_2) ).

thf(2855,plain,
    ! [A: $i] :
      ( ( ( c_Transcendental_Otan @ ( c_Transcendental_Osko__Transcendental__Xtan__total__pi4__1__1 @ A ) )
        = A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[809]) ).

thf(252,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gt__half__sum_0) ).

thf(1639,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A ) @ A ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).

thf(808,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(2853,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)],[808]) ).

thf(548,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(2290,plain,
    class_Ring__and__Field_Oordered__semiring__strict @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).

thf(530,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(2251,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)],[530]) ).

thf(365,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(1903,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)],[365]) ).

thf(601,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult) ).

thf(2406,plain,
    class_OrderedGroup_Omonoid__mult @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).

thf(247,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(1629,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)],[247]) ).

thf(416,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_7) ).

thf(2004,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).

thf(660,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__number__of_0) ).

thf(2526,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).

thf(607,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(2416,plain,
    class_Ring__and__Field_Odivision__by__zero @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).

thf(848,axiom,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
      | ( ( c_Transcendental_Osin @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ A @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__zero__iff_5) ).

thf(2934,plain,
    ! [A: $i] :
      ( ~ ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
      | ( ( c_Transcendental_Osin @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ A @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[848]) ).

thf(485,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Int_OBit1 @ A )
     != ( c_Int_OBit0 @ B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I50_J_0) ).

thf(2152,plain,
    ! [B: $i,A: $i] :
      ( ( c_Int_OBit1 @ A )
     != ( c_Int_OBit0 @ B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).

thf(535,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(2262,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)],[535]) ).

thf(622,axiom,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__pi__half__less__zero_0) ).

thf(2447,plain,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).

thf(418,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__gt__half__sum_0) ).

thf(2009,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).

thf(858,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(2956,plain,
    class_OrderedGroup_Opordered__ab__semigroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[858]) ).

thf(1032,axiom,
    ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__two__pi_0) ).

thf(3324,plain,
    ( ( c_Transcendental_Osin @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1032]) ).

thf(1005,axiom,
    c_HOL_Oord__class_Oless @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__less__4_0) ).

thf(3267,plain,
    c_HOL_Oord__class_Oless @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1005]) ).

thf(681,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(2576,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)],[681]) ).

thf(458,axiom,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__45_0) ).

thf(2095,plain,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).

thf(560,axiom,
    ! [A: $i] :
      ( ( ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal )
        = A )
      | ( 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__abs__def_1) ).

thf(2315,plain,
    ! [A: $i] :
      ( ( ( c_HOL_Oabs__class_Oabs @ A @ tc_RealDef_Oreal )
        = A )
      | ( 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)],[560]) ).

thf(411,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_8) ).

thf(1994,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).

thf(775,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(2779,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)],[775]) ).

thf(589,axiom,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pi__gt__zero_0) ).

thf(2384,plain,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).

thf(636,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(2475,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)],[636]) ).

thf(778,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(2786,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)],[778]) ).

thf(597,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_8) ).

thf(2399,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).

thf(432,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_Int_OBit1 @ A )
       != ( c_Int_OBit1 @ B ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__simps_I51_J_0) ).

thf(2041,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_Int_OBit1 @ A )
       != ( c_Int_OBit1 @ B ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).

thf(713,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(2648,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)],[713]) ).

thf(311,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__add__less__0__iff_1) ).

thf(1777,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).

thf(114,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(1308,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)],[114]) ).

thf(506,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ 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__square__gt__zero_0) ).

thf(2198,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ A @ A @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ B @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ( A
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).

thf(282,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(1706,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)],[282]) ).

thf(67,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(1193,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)],[67]) ).

thf(19,axiom,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff1_1) ).

thf(1077,plain,
    ! [E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ E @ A ) @ C @ A ) @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).

thf(489,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_4) ).

thf(2162,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).

thf(727,axiom,
    class_Ring__and__Field_Osemiring @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring) ).

thf(2680,plain,
    class_Ring__and__Field_Osemiring @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).

thf(498,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ 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 ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_2) ).

thf(2183,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ 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 ) @ C @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).

thf(833,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ominus_0) ).

thf(2902,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
        = ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[833]) ).

thf(469,axiom,
    ( ( c_Transcendental_Osin @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__30_0) ).

thf(2120,plain,
    ( ( c_Transcendental_Osin @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).

thf(361,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(1893,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)],[361]) ).

thf(551,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A )
        = B )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__divide__eq_0) ).

thf(2294,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ C @ A )
        = B )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).

thf(756,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(2739,plain,
    class_Ring__and__Field_Ozero__neq__one @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[756]) ).

thf(644,axiom,
    ! [A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_one__add__one__is__two_0) ).

thf(2494,plain,
    ! [A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_HOL_Oone__class_Oone @ A ) @ A )
        = ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).

thf(171,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__0__less__add__iff_0) ).

thf(1444,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ A @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).

thf(839,axiom,
    c_lessequals @ ( c_Transcendental_Ocos @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__two__le__zero_0) ).

thf(2917,plain,
    c_lessequals @ ( c_Transcendental_Ocos @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[839]) ).

thf(703,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__0__1__iff_0) ).

thf(2623,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).

thf(242,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(1614,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)],[242]) ).

thf(610,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_8) ).

thf(2421,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).

thf(35,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(1116,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)],[35]) ).

thf(42,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(1133,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)],[42]) ).

thf(547,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ B ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_number__of__Bit1_0) ).

thf(2287,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ B ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oone__class_Oone @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).

thf(461,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(2102,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)],[461]) ).

thf(729,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ 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__0__le__divide__iff_2) ).

thf(2683,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oinverse__class_Odivide @ A @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ A @ 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)],[729]) ).

thf(103,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_2) ).

thf(1280,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).

thf(590,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(2385,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)],[590]) ).

thf(82,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(1229,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)],[82]) ).

thf(151,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(1395,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)],[151]) ).

thf(856,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_8) ).

thf(2951,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[856]) ).

thf(754,axiom,
    c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__sqrt__two__gt__one_0) ).

thf(2736,plain,
    c_HOL_Oord__class_Oless @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[754]) ).

thf(436,axiom,
    ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ 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 )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__two__squares__add__zero__iff_2) ).

thf(2050,plain,
    ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ 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 )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).

thf(908,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(3062,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)],[908]) ).

thf(956,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(3164,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)],[956]) ).

thf(198,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(1512,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)],[198]) ).

thf(310,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(1774,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)],[310]) ).

thf(226,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__iff__diff__eq__0_1) ).

thf(1578,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
       != ( c_HOL_Ozero__class_Ozero @ A ) )
      | ( B = C ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).

thf(392,axiom,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Osin @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__diff_0) ).

thf(1957,plain,
    ! [B: $i,A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Osin @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Osin @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).

thf(486,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Ocos @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ B )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ A )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lemma__tan__add1_0) ).

thf(2155,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_Transcendental_Ocos @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ B )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
      | ( ( c_Transcendental_Ocos @ A )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).

thf(532,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(2255,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)],[532]) ).

thf(989,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__numeral__1_0) ).

thf(3232,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[989]) ).

thf(28,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(1097,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)],[28]) ).

thf(687,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__half__sum_0) ).

thf(2587,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ A @ B @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).

thf(232,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(1593,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)],[232]) ).

thf(694,axiom,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Ocomm__monoid__add) ).

thf(2604,plain,
    class_OrderedGroup_Ocomm__monoid__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).

thf(784,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(2800,plain,
    class_OrderedGroup_Opordered__cancel__ab__semigroup__add @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[784]) ).

thf(507,axiom,
    ( ( c_Transcendental_Otan @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__60_0) ).

thf(2201,plain,
    ( ( c_Transcendental_Otan @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_NthRoot_Osqrt @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).

thf(117,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(1314,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)],[117]) ).

thf(568,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(2334,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)],[568]) ).

thf(1010,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(3277,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)],[1010]) ).

thf(760,axiom,
    class_OrderedGroup_Ogroup__add @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__OrderedGroup_Ogroup__add) ).

thf(2746,plain,
    class_OrderedGroup_Ogroup__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[760]) ).

thf(219,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(1561,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)],[219]) ).

thf(608,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(2417,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)],[608]) ).

thf(861,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq__number__of_3) ).

thf(2961,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ D @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[861]) ).

thf(183,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).

thf(1473,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Oab__group__add @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
        = ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).

thf(14,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(1065,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)],[14]) ).

thf(571,axiom,
    ! [A: $i] :
      ( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
      | ( ( c_Transcendental_Ocos @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ A @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__zero__iff_4) ).

thf(2340,plain,
    ! [A: $i] :
      ( ( c_Parity_Oeven__odd__class_Oeven @ A @ tc_nat )
      | ( ( c_Transcendental_Ocos @ ( c_HOL_Otimes__class_Otimes @ ( c_RealDef_Oreal @ A @ tc_nat ) @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
        = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).

thf(714,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__frac__num_0) ).

thf(2651,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Oplus__class_Oplus @ B @ ( c_HOL_Otimes__class_Otimes @ D @ C @ A ) @ A ) @ C @ A ) )
      | ( C
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).

thf(948,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(3145,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)],[948]) ).

thf(708,axiom,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__ge__zero_0) ).

thf(2636,plain,
    ! [A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_Transcendental_Ocos @ A ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).

thf(168,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(1436,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)],[168]) ).

thf(347,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(1859,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)],[347]) ).

thf(277,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( 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_Odiff__left_0) ).

thf(1693,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__algebra @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ D @ A )
        = ( c_HOL_Ominus__class_Ominus @ ( 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)],[277]) ).

thf(447,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(2070,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)],[447]) ).

thf(10,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_2) ).

thf(1056,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).

thf(316,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__less__sum__gt__zero_0) ).

thf(1789,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ ( c_HOL_Oplus__class_Oplus @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).

thf(837,axiom,
    class_Orderings_Olinorder @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_RealDef__Oreal__Orderings_Olinorder) ).

thf(2913,plain,
    class_Orderings_Olinorder @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[837]) ).

thf(456,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(2091,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)],[456]) ).

thf(600,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__monotone__minus__pi__0_H_0) ).

thf(2404,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_Transcendental_Ocos @ A ) @ ( c_Transcendental_Ocos @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ ( c_HOL_Ouminus__class_Ouminus @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).

thf(744,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(2714,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)],[744]) ).

thf(974,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(3196,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)],[974]) ).

thf(360,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(1891,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)],[360]) ).

thf(423,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ 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_divide__le__0__1__iff_1) ).

thf(2021,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ 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)],[423]) ).

thf(240,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(1610,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)],[240]) ).

thf(941,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_add__numeral__0_0) ).

thf(3128,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_Int_Onumber__class_Onumber__of @ c_Int_OPls @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[941]) ).

thf(831,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(2898,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)],[831]) ).

thf(995,axiom,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tan__monotone_H_1) ).

thf(3245,plain,
    ! [B: $i,A: $i] :
      ( ( c_HOL_Oord__class_Oless @ A @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Transcendental_Otan @ A ) @ ( c_Transcendental_Otan @ B ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ B @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ A @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[995]) ).

thf(285,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(1713,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)],[285]) ).

thf(640,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ B @ A )
        = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mult__numeral__1_0) ).

thf(2484,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ c_Int_OPls ) @ A ) @ B @ A )
        = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).

thf(539,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__divide__eq_5) ).

thf(2270,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).

thf(37,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(1120,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)],[37]) ).

thf(26,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(1093,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)],[26]) ).

thf(576,axiom,
    class_Int_Onumber @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Int_Onumber) ).

thf(2353,plain,
    class_Int_Onumber @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).

thf(789,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_6) ).

thf(2810,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[789]) ).

thf(133,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(1352,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)],[133]) ).

thf(752,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(2731,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)],[752]) ).

thf(863,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(2966,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)],[863]) ).

thf(614,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(2430,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)],[614]) ).

thf(906,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__0__1__iff_0) ).

thf(3057,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_Odivide @ ( c_HOL_Oone__class_Oone @ A ) @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[906]) ).

thf(806,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(2847,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)],[806]) ).

thf(401,axiom,
    ( ( c_Transcendental_Oarctan @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_arctan__zero__zero_0) ).

thf(1976,plain,
    ( ( c_Transcendental_Oarctan @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).

thf(214,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(1550,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)],[214]) ).

thf(914,axiom,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Ominus__class_Ominus @ A @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__periodic__pi__diff_0) ).

thf(3076,plain,
    ! [A: $i] :
      ( ( c_Transcendental_Osin @ ( c_HOL_Ominus__class_Ominus @ A @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
      = ( c_HOL_Ouminus__class_Ouminus @ ( c_Transcendental_Osin @ A ) @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[914]) ).

thf(934,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of_1) ).

thf(3113,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[934]) ).

thf(765,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide_Ozero_0) ).

thf(2754,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_RealVector_Oreal__normed__field @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[765]) ).

thf(723,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(2672,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)],[723]) ).

thf(386,axiom,
    ! [B: $i,A: $i] :
      ( ( ( c_RealDef_Oreal @ A @ tc_nat )
       != ( c_RealDef_Oreal @ B @ tc_nat ) )
      | ( A = B ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__of__nat__inject_0) ).

thf(1944,plain,
    ! [B: $i,A: $i] :
      ( ( ( c_RealDef_Oreal @ A @ tc_nat )
       != ( c_RealDef_Oreal @ B @ tc_nat ) )
      | ( A = B ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).

thf(395,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(1962,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)],[395]) ).

thf(733,axiom,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__3over2__pi_0) ).

thf(2690,plain,
    ( ( c_Transcendental_Ocos @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Oinverse__class_Odivide @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit1 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) )
    = ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).

thf(616,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of1_9) ).

thf(2436,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ C @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).

thf(160,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__divide__right_0) ).

thf(1416,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ A )
        = ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).

thf(454,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__strict__left__mono_0) ).

thf(2087,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_HOL_Oinverse__class_Odivide @ B @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_HOL_Otimes__class_Otimes @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).

thf(633,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq_1) ).

thf(2470,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A )
      | ~ ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ D @ C @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).

thf(1018,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__le__eq__number__of1_8) ).

thf(3296,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ~ ( c_lessequals @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1018]) ).

thf(495,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(2177,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)],[495]) ).

thf(351,axiom,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
        = ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__minus__commute_0) ).

thf(1870,plain,
    ! [C: $i,B: $i,A: $i] :
      ( ~ ( class_OrderedGroup_Opordered__ab__group__add__abs @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
        = ( c_HOL_Oabs__class_Oabs @ ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).

thf(124,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(1331,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)],[124]) ).

thf(238,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(1606,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)],[238]) ).

thf(676,axiom,
    ( ( c_Transcendental_Ocos @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) )
   != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cos__two__neq__zero_0) ).

thf(2563,plain,
    ( ( c_Transcendental_Ocos @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) )
   != ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).

thf(822,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq_6) ).

thf(2881,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( c_lessequals @ B @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ B @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[822]) ).

thf(980,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(3212,plain,
    class_OrderedGroup_Opordered__ab__group__add @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[980]) ).

thf(1020,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of_5) ).

thf(3299,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ C @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ D @ A ) @ C @ A ) @ B @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1020]) ).

thf(294,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(1737,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)],[294]) ).

thf(925,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_8) ).

thf(3096,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A )
      | ~ ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Otimes__class_Otimes @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[925]) ).

thf(509,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_right__distrib__number__of_0) ).

thf(2206,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Osemiring @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oplus__class_Oplus @ C @ D @ A ) @ A )
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ C @ A ) @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).

thf(272,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(1681,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)],[272]) ).

thf(825,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(2887,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)],[825]) ).

thf(422,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__eq__eq_1) ).

thf(2018,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Ofield @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ( ( c_HOL_Oinverse__class_Odivide @ B @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
        = ( c_HOL_Ozero__class_Ozero @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).

thf(814,axiom,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_m2pi__less__pi_0) ).

thf(2866,plain,
    c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) @ c_Transcendental_Opi @ tc_RealDef_Oreal,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[814]) ).

thf(800,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(2832,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)],[800]) ).

thf(617,axiom,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_real__le__eq__diff_0) ).

thf(2438,plain,
    ! [B: $i,A: $i] :
      ( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ tc_RealDef_Oreal ) @ ( c_HOL_Ozero__class_Ozero @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal )
      | ~ ( c_lessequals @ A @ B @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).

thf(189,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(1490,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)],[189]) ).

thf(552,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_divide__less__eq__number__of1_1) ).

thf(2297,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Otimes__class_Otimes @ B @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ D @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A )
      | ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Oinverse__class_Odivide @ D @ ( c_Int_Onumber__class_Onumber__of @ C @ A ) @ A ) @ B @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).

thf(700,axiom,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs__number__of_1) ).

thf(2615,plain,
    ! [B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__idom @ A )
      | ~ ( class_Int_Onumber__ring @ A )
      | ( ( c_HOL_Oabs__class_Oabs @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ A )
        = ( c_Int_Onumber__class_Onumber__of @ B @ A ) )
      | ( c_HOL_Oord__class_Oless @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Ozero__class_Ozero @ A ) @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).

thf(308,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(1769,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)],[308]) ).

thf(1028,axiom,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__OrderedGroup_Omonoid__mult) ).

thf(3316,plain,
    class_OrderedGroup_Omonoid__mult @ tc_nat,
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[1028]) ).

thf(24,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(1088,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)],[24]) ).

thf(492,axiom,
    ( ( c_Transcendental_Osin @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sin__pi__half_0) ).

thf(2170,plain,
    ( ( c_Transcendental_Osin @ ( c_HOL_Oinverse__class_Odivide @ c_Transcendental_Opi @ ( c_Int_Onumber__class_Onumber__of @ ( c_Int_OBit0 @ ( c_Int_OBit1 @ c_Int_OPls ) ) @ tc_RealDef_Oreal ) @ tc_RealDef_Oreal ) )
    = ( c_HOL_Oone__class_Oone @ tc_RealDef_Oreal ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).

thf(801,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(2834,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)],[801]) ).

thf(503,axiom,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__divide__eq__number__of_6) ).

thf(2191,plain,
    ! [D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oordered__field @ A )
      | ~ ( class_Ring__and__Field_Odivision__by__zero @ A )
      | ~ ( class_Int_Onumber @ A )
      | ( c_lessequals @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ ( c_HOL_Oinverse__class_Odivide @ C @ D @ A ) @ A )
      | ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ A ) @ D @ A )
      | ~ ( c_lessequals @ ( c_HOL_Otimes__class_Otimes @ ( c_Int_Onumber__class_Onumber__of @ B @ A ) @ D @ A ) @ C @ A ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).

thf(173,axiom,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
       != ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
      | ( D
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__add__iff2_0) ).

thf(1449,plain,
    ! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
      ( ~ ( class_Ring__and__Field_Oring @ A )
      | ( ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ B @ C @ A ) @ D @ A )
       != ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ E @ C @ A ) @ F @ A ) )
      | ( D
        = ( c_HOL_Oplus__class_Oplus @ ( c_HOL_Otimes__class_Otimes @ ( c_HOL_Ominus__class_Ominus @ E @ B @ A ) @ C @ A ) @ F @ A ) ) ),
    inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).

thf(370,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(1912,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)],[370]) ).

thf(894,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(3035,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)],[894]) ).

thf(3332,plain,
    $false,
    inference(e,[status(thm)],[3021,1411,1469,2336,1633,1559,1729,1237,2463,2480,2559,2544,2331,1950,2280,1686,1036,2630,1586,1501,1879,1337,1718,1168,2306,3053,2072,1767,2595,2499,1211,2512,1924,3317,1290,1068,2381,1269,1793,1041,1173,1855,1200,1750,3185,2117,1596,2104,2808,1522,2395,2908,2062,2953,2590,1401,2947,1569,3098,1073,3012,1205,2282,1591,1608,3135,3044,2448,2141,1761,1954,2146,1458,2607,2686,1756,1310,3004,2035,2740,2918,1867,3175,1164,1999,1988,2459,1507,1222,1095,1196,1746,1914,2227,1441,1046,3281,2082,1366,2516,2819,2531,2869,2957,2348,2723,2491,2548,1782,1650,1921,3140,1724,2067,1529,1967,2136,1703,1623,1254,2654,2328,3029,3275,2667,3046,1826,3089,2466,2703,1409,3204,3263,1287,3221,2814,1985,2698,3131,1660,1298,1907,2501,2444,1264,2217,1323,3148,2185,1455,1832,2897,1191,1462,3043,2571,2356,1545,1922,1379,1147,1247,2767,2929,2158,1641,3180,1875,3231,2533,1847,3099,1800,2373,1347,1741,1398,3312,1931,3014,2730,2301,1815,1494,1232,3268,3258,2456,2222,2027,1811,3295,1334,1136,1151,2034,1581,1183,1664,2794,2451,2236,1864,2122,1828,1978,2291,1383,1960,3290,2777,3152,2508,2058,2367,1377,1886,2523,1526,3243,3226,2804,1600,1242,2392,2718,1564,2762,2618,3189,2772,3157,2242,1345,2750,1405,1696,3184,2586,2011,3229,2473,1691,2646,1306,3186,1338,2047,2737,2641,2621,2905,3037,1604,2922,3301,3303,2364,2164,1915,1708,2093,2232,2307,2589,1091,2601,2249,2541,1355,1123,1676,2147,1666,1487,2937,3154,2032,3207,1883,2705,2264,2409,1387,1900,1343,2560,3239,3069,1824,1370,2414,3250,2132,2890,3307,3166,1938,2628,1920,2433,3198,1178,2872,1296,2609,2179,1656,2213,1392,1910,1573,2769,1106,1837,1602,2663,1555,2826,3314,2068,1819,3028,3050,2211,1407,2313,1128,1350,3105,1234,1983,1143,2100,2801,2359,3218,2692,1540,1878,2858,3119,3078,3237,2268,1259,3122,2990,1534,1953,2685,1111,1970,3102,1672,2638,1118,3176,3087,3018,1567,1683,1329,3143,1361,1942,2323,2830,1424,2080,1160,2877,1082,2023,3326,3094,1739,2419,1075,2196,2240,1937,2613,3032,1791,2172,1214,3194,2038,1446,1889,1644,1612,1039,2978,2472,2781,1419,2304,2836,1131,2505,2566,1947,1852,3115,1715,3064,2272,2968,2285,2504,2932,2125,1099,1478,1249,2519,2536,2681,2487,2845,2598,3059,2900,2387,1668,1974,2581,1060,1050,2006,2497,1429,3247,2862,2052,2482,3109,1979,3074,3083,3201,1759,2370,3215,2926,1086,2546,1779,3279,2057,2440,1515,1895,1732,1434,1857,1991,2788,1318,1202,2203,2883,3173,2748,1170,2963,3321,1035,1466,2402,2089,3190,2189,2995,2338,1996,2423,2529,2144,1278,1648,2001,2413,2292,3257,1273,3111,1631,2260,1727,1510,1959,2556,2253,2275,2149,1548,1927,1301,2734,2894,1374,1154,3187,2727,2048,2225,3086,2806,1403,2716,1965,1520,2134,2970,3319,1784,3255,2789,1125,2188,2981,1620,2489,1652,3081,1929,3266,2674,2016,2514,2568,1795,1701,2398,1226,2695,1256,2959,3213,3223,1139,2326,3051,1271,1312,1058,1239,1765,1897,1224,2573,3023,2193,1786,3118,2220,1635,3002,2442,2753,3091,1464,2510,2346,2361,2721,2538,2084,2987,1048,2669,3101,2521,1282,2478,2151,2229,2774,3287,1524,2097,3270,2257,1589,2246,1492,2299,2116,2839,1771,2943,2945,2378,3182,2896,1571,1439,2065,1175,2824,2182,1471,2742,2605,2111,1993,1862,1460,2664,1381,1688,2025,2812,1080,3133,3055,1557,2343,2625,1909,1162,2446,2757,2593,3006,1149,3298,1293,2278,2553,2461,2974,2842,3150,2329,2710,2911,2075,2350,2139,2931,2244,1496,2999,2867,2506,1198,1841,2725,2401,1699,2765,1044,2550,1245,3159,2064,3241,1113,2797,3016,2633,3310,1364,2390,3178,1102,2984,1805,1413,2054,2239,1809,1662,1208,3293,2878,2234,2449,3048,1340,1145,1181,2582,1626,3009,2914,2816,1583,1304,1873,3193,1166,2107,2318,2784,3161,1905,2942,1748,1798,2397,1070,2661,2143,3260,1252,1368,1531,2863,1598,2375,1156,2060,1743,2678,2518,2821,3209,1753,2407,1267,2850,1484,2160,2920,1262,2128,1658,1679,3329,2354,2656,1711,3019,2747,1053,1499,1987,2454,3305,1432,1813,1452,1637,2688,3273,1188,1186,3026,2429,1830,1763,3127,1538,2701,1218,3041,2468,1220,1934,2411,1849,2113,1802,2379,1955,2579,1427,1504,1670,2030,2939,3071,1881,2266,2584,1617,2675,1358,2247,1543,3107,1141,3124,2426,2992,1536,1981,1284,2975,1972,2320,2711,2860,2949,1372,2892,1839,3067,2885,1654,2611,2643,2658,1998,2875,3168,1940,3284,2760,1421,2013,2924,1918,1316,1084,2045,3092,2696,1553,2870,2828,1817,3171,2078,1321,1834,2310,1844,2215,1517,1216,2209,2743,2997,2187,2110,1390,1575,1734,2792,1807,1108,3039,1276,1646,1326,2707,2167,2554,1062,1481,2823,2971,3235,1822,2130,3136,3252,3085,2988,1385,1721,2174,2283,1476,1674,2855,1639,2853,2290,2251,1903,2406,1629,2004,2526,2416,2934,2152,2262,2447,2009,2956,3324,3267,2576,2095,2315,1994,2779,2384,2475,2786,2399,2041,2648,1777,1308,2198,1706,1193,1077,2162,2680,2183,2902,2120,1893,2294,2739,2494,1444,2917,2623,1614,2421,1116,1133,2287,2102,2683,1280,2385,1229,1395,2951,2736,2050,3062,3164,1512,1774,1578,1957,2155,2255,3232,1097,2587,1593,2604,2800,2201,1314,2334,3277,2746,1561,2417,2961,1473,1065,2340,2651,3145,2636,1436,1859,1693,2070,1056,1789,2913,2091,2404,2714,3196,1891,2021,1610,3128,2898,3245,1713,2484,2270,1120,1093,2353,2810,1352,2731,2966,2430,3057,2847,1976,1550,3076,3113,2754,2672,1944,1962,2690,2436,1416,2087,2470,3296,2177,1870,1331,1606,2563,2881,3212,3299,1737,3096,2206,1681,2887,2018,2866,2832,2438,1490,2297,2615,1769,3316,1088,2170,2834,2191,1449,1912,3035]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.12  % Problem  : SWV603-1 : TPTP v8.2.0. Released v4.1.0.
% 0.10/0.15  % Command  : run_Leo-III %s %d
% 0.14/0.36  % Computer : n019.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Sun May 19 06:31:09 EDT 2024
% 0.14/0.36  % CPUTime  : 
% 0.97/0.88  % [INFO] 	 Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ... 
% 1.64/1.17  % [INFO] 	 Parsing done (295ms). 
% 2.01/1.18  % [INFO] 	 Running in sequential loop mode. 
% 2.41/1.42  % [INFO] 	 eprover registered as external prover. 
% 2.41/1.42  % [INFO] 	 cvc4 registered as external prover. 
% 2.41/1.43  % [INFO] 	 Scanning for conjecture ... 
% 2.85/1.58  % [INFO] 	 Found a conjecture (or negated_conjecture) and 1109 axioms. Running axiom selection ... 
% 3.57/1.76  % [INFO] 	 Axiom selection finished. Selected 1032 axioms (removed 77 axioms). 
% 4.85/2.00  % [INFO] 	 Problem is propositional (TPTP CNF). 
% 4.85/2.02  % [INFO] 	 Type checking passed. 
% 4.85/2.02  % [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 ... 
% 15.17/4.63  % External prover 'e' found a proof!
% 15.17/4.63  % [INFO] 	 Killing All external provers ... 
% 15.17/4.63  % Time passed: 4129ms (effective reasoning time: 3446ms)
% 15.17/4.64  % Axioms used in derivation (1032): cls_abs__le__zero__iff_0, cls_divide__le__eq__number__of1_9, cls_divide__le__eq__number__of_9, cls_cos__diff_0, cls_xt1_I9_J_0, cls_le__divide__eq_8, cls_linorder__antisym__conv2_1, cls_add__cancel__end_1, cls_add__pos__nonneg_0, cls_mult__numeral__1__right_0, clsarity_RealDef__Oreal__Ring__and__Field_Oabs__if, cls_sin__le__one_0, cls_neg__0__le__iff__le_1, cls_le__divide__eq_3, clsarity_nat__OrderedGroup_Oab__semigroup__add, cls_order__le__less__trans_0, cls_less__divide__eq_3, cls_not__one__less__zero_0, cls_mult__less__cancel__left__disj_5, cls_less__iff__diff__less__0_0, cls_real__mult__is__one_1, clsarity_RealDef__Oreal__OrderedGroup_Oordered__ab__group__add, cls_cos__monotone__minus__pi__0_H_0, cls_add__0__left_0, cls_sin__two__pi_0, cls_cos__30_0, cls_minus__le__iff_0, cls_divide__eq__eq_3, cls_eq__add__iff2_1, cls_mult__zero__right_0, cls_zero__less__one_0, cls_abs__div__pos_0, cls_abs__if__lattice_0, cls_order__eq__iff_0, cls_sin__periodic__pi_0, cls_zero__less__divide__iff_5, cls_divide__eq__eq__number__of_4, cls_less__divide__eq__number__of1_6, cls_le__minus__self__iff_0, cls_abs__le__iff_2, cls_divide__le__eq_2, cls_tan__monotone_H_1, cls_divide__pos__pos_0, cls_mult__imp__le__div__pos_0, clsarity_RealDef__Oreal__Orderings_Opreorder, cls_class__ringb_Oadd__r0__iff_1, cls_mult__nonneg__nonneg_0, cls_mult__2__right_0, cls_eq__divide__eq__number__of1_4, 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_tan__minus_0, cls_sin__less__zero_0, cls_DERIV__mult__lemma_0, cls_order__less__le__trans_0, cls_divide__less__0__iff_0, clsarity_RealDef__Oreal__RealVector_Oreal__field, cls_comm__semiring__class_Odistrib_0, cls_tan__total__pi4_2, cls_real__of__nat__ge__zero_0, cls_real__le__add__half__cancel_0, cls_abs__of__nonneg_0, cls_real__mult__le__cancel__iff1_0, cls_xt1_I12_J_0, cls_mult__less__cancel__right__disj_0, cls_m2pi__less__pi_0, cls_mult__nonneg__nonpos2_0, cls_real__sum__squares__cancel_0, cls_real__less__def_1, cls_sum__squares__eq__zero__iff_0, cls_eq__divide__2__times__iff_1, cls_Bit0__Pls_0, cls_left__minus_0, cls_divide__le__eq__number__of_4, cls_minus__zero_0, cls_number__of__Bit1_0, cls_Lim_Ominus__diff__minus_0, cls_mult_Odiff__left_0, cls_real__mult__assoc_0, cls_divide__self_0, cls_real__sqrt__zero_0, cls_square__eq__iff_1, cls_sin__45_0, cls_divide__nonpos__neg_0, cls_class__semiring_Osemiring__rules_I9_J_0, cls_real__mult__le__cancel__iff2_1, cls_le__divide__eq__number__of1_0, cls_mult__less__cancel__left__disj_1, cls_zero__le__one_0, cls_real__0__le__divide__iff_0, cls_comp__arith_I112_J_0, cls_half_0, cls_add__increasing2_0, cls_divide__numeral__1_0, cls_less__half__sum_0, cls_abs__diff__triangle__ineq_0, cls_zero__le__mult__iff_3, cls_divide__less__eq__number__of1_5, cls_le__divide__eq__number__of_6, cls_real__sqrt__mult__self__sum__ge__zero_0, cls_less__divide__eq__number__of_8, cls_right__distrib__number__of_0, cls_not__sum__squares__lt__zero_0, cls_class__semiring_Osemiring__rules_I20_J_0, cls_diff__add__cancel_0, cls_abs__triangle__ineq2_0, cls_tan__zero_0, cls_linorder__neqE_0, cls_real__sqrt__gt__0__iff_1, cls_divide__1_0, cls_add__strict__right__mono_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__cancel__semiring, cls_cos__zero__iff_5, cls_divide__le__eq__number__of1_4, cls_real__add__le__0__iff_1, cls_pos__add__strict_0, cls_abs__add__one__gt__zero_0, cls_zero__le__divide__iff_2, cls_abs__minus__le__zero_0, cls_half__gt__zero_0, cls_class__semiring_Osemiring__rules_I21_J_0, cls_less__divide__eq__number__of_3, cls_real__minus__half__eq_0, cls_class__semiring_Osemiring__rules_I10_J_0, cls_add__imp__eq_0, cls_divide__le__eq_7, cls_minus__diff__eq_0, cls_frac__le_0, cls_left__distrib__number__of_0, cls_mult__nonpos__nonneg_0, cls_divide__Numeral1_0, cls_add__le__cancel__right_1, cls_minus__le__self__iff_0, cls_number__of__Pls_0, cls_divide__less__eq_4, cls_minus__add__distrib_0, cls_zero__less__divide__iff_0, cls_abs__eq__mult_1, cls_add__le__cancel__left_1, cls_divide__le__eq_8, cls_real__le__trans_0, cls_real__0__le__divide__iff_4, cls_divide__less__eq__number__of1_0, clsarity_RealDef__Oreal__OrderedGroup_Oab__group__add, cls_tan__45_0, cls_divide__less__eq__number__of_1, clsarity_nat__OrderedGroup_Omonoid__add, cls_le__divide__eq__number__of1_5, cls_abs__mult__less_0, cls_divide__le__0__1__iff_1, cls_real__sqrt__lt__0__iff_1, cls_real__le__eq__diff_1, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__semigroup__add, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__add, cls_real__mult__less__iff1_0, cls_tan__less__zero_0, cls_divide__Numeral0_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__field, clsarity_RealDef__Oreal__OrderedGroup_Omonoid__add, cls_minus__divide__right_0, cls_cos__zero__lemma_1, clsarity_nat__Orderings_Olinorder, cls_minus__minus_0, cls_sum__squares__ge__zero_0, cls_mult__less__imp__less__right_0, cls_le__eq__neg_0, cls_comm__monoid__add_Omult__assoc_0, cls_order__less__trans_0, cls_class__semiring_Osemiring__rules_I14_J_0, cls_neg__less__iff__less_1, cls_add__cancel__21_1, cls_eq__divide__eq__number__of_1, cls_left__diff__distrib__number__of_0, cls_cos__two__pi_0, clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add__abs, cls_mult__le__cancel__left__pos_0, cls_sin__30_0, cls_eq__divide__eq__number__of_4, cls_cos__le__one_0, cls_divide__eq__eq_0, cls_mult__nonpos__nonpos_0, cls_abs__sum__triangle__ineq_0, cls_class__ring_Osub__add_0, cls_class__ringb_Onoteq__reduce_0, cls_rel__simps_I49_J_0, cls_comm__monoid__add_Omult__1__right_0, cls_pi__not__less__zero_0, cls_abs__cos__le__one_0, cls_add__nonpos__neg_0, cls_abs__of__pos_0, cls_divide__less__eq_5, cls_real__gt__half__sum_0, cls_real__mult__le__cancel__iff2_0, cls_divide__less__eq__number__of1_6, cls_le__real__sqrt__sumsq_0, cls_arctan__zero__zero_0, clsarity_nat__Ring__and__Field_Oordered__comm__semiring__strict, cls_add__left__cancel_0, cls_less__minus__iff_0, cls_lemma__MVT_0, cls_minus__unique_0, cls_split__mult__neg__le_0, cls_divide__le__0__iff_3, cls_divide__le__eq__number__of_5, cls_less__divide__eq_4, cls_real__sqrt__le__1__iff_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono, cls_abs__add__one__not__less__self_0, cls_add__nonneg__pos_0, cls_divide__strict__left__mono_0, cls_mult__less__cancel__left__disj_4, cls_class__ringb_Oadd__mul__solve_1, cls_mult__less__imp__less__left_0, cls_real__minus__mult__self__le_0, cls_real__sqrt__ge__0__iff_1, cls_sum__squares__le__zero__iff_1, cls_le__divide__eq__number__of1_9, cls_cos__periodic_0, cls_abs__le__interval__iff_0, cls_mult__less__cancel__right__disj_3, cls_real__sqrt__lt__1__iff_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_eq__add__iff1_0, clsarity_RealDef__Oreal__OrderedGroup_Oab__semigroup__mult, 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_zero__less__double__add__iff__zero__less__single__add_0, cls_divide__eq__eq_4, clsarity_nat__OrderedGroup_Omonoid__mult, cls_add__right__mono_0, cls_less__divide__eq__number__of1_2, cls_cos__diff2_0, cls_real__average__minus__second_0, cls_less__iff__diff__less__0_1, cls_real__divide__square__eq_0, cls_eq__divide__eq_4, cls_mult__mono_0, cls_pi__half__gt__zero_0, cls_ab__left__minus_0, cls_class__semiring_Omul__0_0, cls_right__inverse__eq_0, cls_rel__simps_I38_J_1, clsarity_nat__Ring__and__Field_Oordered__semiring, cls_neg__equal__iff__equal_0, cls_frac__eq__eq_0, cls_real__squared__diff__one__factored_0, cls_divide__less__eq__number__of_6, cls_real__of__nat__inject_0, cls_one__add__one__is__two_0, 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, cls_less__add__iff2_0, clsarity_nat__Ring__and__Field_Ocomm__semiring, cls_mult_Ozero__left_0, cls_cos__two__le__zero_0, cls_divide__neg__neg_0, cls_mult__2_0, cls_less__divide__eq__number__of1_0, cls_minus__sin__cos__eq_0, cls_order__less__asym_H_0, cls_double__eq__0__iff_1, cls_eq__number__of_0, cls_abs__minus__add__cancel_0, cls_real__le__linear_0, cls_mult__strict__right__mono_0, cls_divide__less__eq__number__of1_8, cls_class__semiring_Omul__c_0, cls_tan__total__pi4_1, cls_real__sqrt__eq__0__iff_0, cls_mult__pos__neg_0, cls_order__eq__refl_0, cls_zero__le__mult__iff_0, cls_le__divide__eq__number__of_7, cls_divide__eq__eq__number__of1_0, cls_mult__strict__mono_0, cls_pi__ge__zero_0, cls_order__le__less_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__mono1, cls_mult_Ozero__right_0, cls_mult__left__mono_0, cls_divide__strict__left__mono__neg_0, cls_real__less__sum__gt__zero_0, cls_linorder__antisym__conv1_0, clsarity_RealDef__Oreal__Ring__and__Field_Omult__zero, cls_right__minus__eq_0, cls_divide__le__eq__number__of_8, cls_sin__pi__half_0, 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, cls_real__sqrt__two__gt__zero_0, cls_add__cancel__end_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_neg__0__le__iff__le_0, cls_minus__less__iff_1, cls_real__sum__of__halves_0, cls_class__semiring_Osemiring__rules_I12_J_0, cls_divide__left__mono__neg_0, cls_real__mult__is__one_2, cls_less__divide__eq_7, cls_le__divide__eq_7, cls_eq__divide__eq__number__of1_3, cls_abs__eq__mult_0, cls_abs__diff__less__iff_1, cls_mult__right_Oadd_0, cls_arctan__tan_0, cls_minus__add__cancel_0, cls_real__less__def_0, cls_divide__right__mono_0, cls_divide__right__mono__neg_0, cls_divide__le__eq__number__of1_5, cls_xt1_I10_J_0, cls_le__divide__eq_2, cls_add__less__cancel__right_1, cls_add__divide__distrib_0, cls_divide__le__eq_3, cls_not__less__iff__gr__or__eq_0, cls_divide__le__eq__number__of1_6, clsarity_RealDef__Oreal__Int_Onumber, cls_no__zero__divisors_0, cls_abs__minus__commute_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__ring__strict, cls_mult__frac__num_0, cls_numeral__1__eq__1_0, cls_zero__le__mult__iff_4, cls_neg__less__eq__nonneg_1, cls_zero__le__double__add__iff__zero__le__single__add_1, cls_less__le__not__le_2, cls_ab__semigroup__add__class_Oadd__ac_I1_J_0, cls_divide__neg__pos_0, cls_real__sqrt__lt__1__iff_1, cls_real__sqrt__abs2_0, cls_real__add__left__mono_0, cls_add__left__mono_0, clsarity_RealDef__Oreal__Ring__and__Field_Odivision__by__zero, cls_le__minus__iff_0, cls_add__nonneg__eq__0__iff_0, cls_less__divide__eq__number__of_7, cls_neg__less__eq__nonneg_0, cls_rel__simps_I39_J_0, cls_sin__ge__zero_0, cls_le__divide__eq__number__of_3, clsarity_nat__OrderedGroup_Opordered__cancel__ab__semigroup__add, cls_divide__less__eq_0, cls_class__semiring_Osemiring__rules_I6_J_0, cls_mult__frac__frac_0, cls_class__semiring_Osemiring__rules_I2_J_0, cls_ab__semigroup__mult__class_Omult__ac_I1_J_0, cls_real__le__add__half__cancel_1, cls_abs__le__interval__iff_2, cls_mult__1__right_0, cls_divide__less__eq__number__of_0, cls_less__divide__eq_2, cls_real__add__minus__iff_0, cls_combine__common__factor_0, cls_sin__zero__iff_5, clsarity_RealDef__Oreal__Ring__and__Field_Olordered__ring, cls_divide__less__eq__number__of1_2, cls_divide__eq__eq__number__of_3, cls_add__strict__left__mono_0, cls_real__abs__def_0, cls_estimate__by__abs_0, clsarity_nat__OrderedGroup_Ocomm__monoid__mult, cls_pi__gt__zero_0, cls_real__sqrt__less__iff_1, cls_mult__le__0__iff_0, cls_add__le__less__mono_0, cls_le__divide__eq__number__of1_6, cls_le__iff__diff__le__0_0, cls_real__le__refl_0, cls_mult__neg__pos_0, cls_pi__less__4_0, cls_mult__left_Odiff_0, cls_less__add__iff1_0, cls_sin__gt__zero_0, cls_zero__less__divide__iff_1, cls_mult__right__le__imp__le_0, cls_tan__30_0, cls_abs__eq__0_0, cls_divide__eq__eq__number__of1_3, cls_divide__less__eq__number__of1_7, cls_diff__minus_0, cls_divide__le__eq__number__of_0, clsarity_RealDef__Oreal__OrderedGroup_Ocancel__ab__semigroup__add, cls_abs__ge__minus__self_0, cls_real__mult__less__mono2_0, cls_real__sqrt__ge__zero_0, cls_mult__pos__neg2_0, cls_real__sum__gt__zero__less_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring, cls_divide__le__eq__number__of_1, clsarity_RealDef__Oreal__Orderings_Olinorder, cls_class__semiring_Osemiring__rules_I15_J_0, cls_mult__mono1_0, cls_mult__less__cancel__left__disj_0, cls_class__semiring_Oadd__a_0, cls_minus__mult__commute_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add__imp__le, cls_le__minus__iff_1, cls_zero__le__divide__iff_3, cls_eq__divide__2__times__iff_0, cls_class__ringb_Onoteq__reduce_1, cls_neg__le__0__iff__le_0, cls_rel__simps_I38_J_0, cls_le__eq__neg_1, cls_le__add__iff1_1, cls_class__semiring_Osemiring__rules_I19_J_0, cls_abs__diff__less__iff_2, cls_xt1_I8_J_0, cls_mult__le__cancel__left__pos_1, cls_less__add__iff2_1, cls_eq__divide__eq_3, cls_pi__half__neq__two_0, cls_real__less__half__sum_0, cls_tan__periodic__n_0, cls_class__semiring_Oadd__0_0, cls_comm__monoid__add_Omult__commute_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_diff__def_0, cls_real__sum__square__gt__zero_0, cls_eq__divide__eq_0, cls_mult_Odiff__right_0, clsarity_nat__Ring__and__Field_Opordered__cancel__semiring, cls_mult__le__cancel__left__neg_1, cls_less__divide__eq__number__of1_3, cls_zero__less__mult__pos_0, cls_divide__self__if_1, cls_mult__le__0__iff_1, cls_class__semiring_Osemiring__rules_I1_J_0, clsarity_nat__Ring__and__Field_Ozero__neq__one, cls_less__divide__eq__number__of_4, cls_cos__45_0, cls_split__mult__pos__le_0, cls_pi__ge__two_0, cls_sum__squares__le__zero__iff_2, cls_divide_Ozero_0, cls_divide__self__if_0, cls_real__sqrt__ge__1__iff_0, cls_le__divide__eq__number__of1_2, cls_class__semiring_Osemiring__rules_I17_J_0, cls_cos__zero__iff_4, cls_mult__imp__div__pos__le_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__group__add__abs, cls_linorder__linear_0, cls_cos__arctan__not__zero_0, cls_tan__def_0, clsarity_RealDef__Oreal__Int_Oring__char__0, cls_real__sqrt__gt__1__iff_1, cls_nonzero__minus__divide__right_0, cls_sum__squares__eq__zero__iff_1, clsarity_nat__Ring__and__Field_Omult__mono, cls_zero__le__divide__iff_5, cls_abs__idempotent_0, cls_mult__le__0__iff_4, cls_sin__npi_0, cls_real__mult__less__iff1_1, cls_zero__less__two_0, cls_mult_Ominus__right_0, cls_sin__add_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_class__ringb_Oadd__mul__solve_0, cls_eq__divide__eq__number__of_3, cls_add__strict__mono_0, cls_real__0__le__divide__iff_3, cls_neg__0__less__iff__less_0, cls_real__add__eq__0__iff_1, cls_neg__less__0__iff__less_0, cls_tan__monotone_H_0, cls_neg__equal__0__iff__equal_0, cls_tan__periodic__pi_0, cls_divide__less__0__iff_3, cls_mult__less__cancel__right__disj_2, cls_minus__le__self__iff_1, cls_add__cancel__21_0, cls_order__trans_0, clsarity_nat__Ring__and__Field_Ocomm__semiring__1, cls_arctan_0, cls_divide__nonneg__neg_0, cls_mult__numeral__1_0, cls_mult__strict__left__mono_0, cls_sum__squares__gt__zero__iff_2, cls_divide__le__0__iff_2, cls_real__0__le__add__iff_1, cls_divide__less__eq__number__of_7, cls_real__mult__order_0, cls_real__sqrt__le__0__iff_0, cls_divide__less__eq_8, cls_sin__cos__squared__add3_0, cls_tan__add_0, cls_arctan__add_0, cls_order__antisym_0, cls_real__0__less__add__iff_1, cls_divide__le__eq_6, clsarity_nat__OrderedGroup_Ocancel__semigroup__add, cls_eq__add__iff1_1, cls_minus__pi__half__less__zero_0, cls_less__divide__eq__number__of1_7, cls_divide__less__eq_1, cls_less__divide__eq__number__of_0, cls_mult__left__less__imp__less_0, cls_le__number__of__eq__not__less_1, cls_ab__diff__minus_0, cls_class__semiring_Omul__d_0, cls_neg__equal__zero_1, cls_divide__eq__eq__number__of_0, cls_abs__minus__cancel_0, cls_linorder__antisym__conv1_1, cls_arctan__minus_0, cls_real__add__eq__0__iff_0, cls_add__frac__eq_0, cls_no__zero__divirors__neq0_0, cls_sin__bound__lemma_0, cls_mult__right_Ominus_0, cls_sin__periodic__pi2_0, cls_diff__self_0, cls_mult__le__0__iff_5, clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__add, cls_mult__strict__mono_H_0, cls_sin__gt__zero__pi_0, cls_double__number__of__Bit0_0, cls_zero__neq__one_0, cls_group__add__class_Odiff__0_0, cls_abs__if_1, cls_class__semiring_Osemiring__rules_I5_J_0, cls_less__divide__eq_5, cls_split__mult__pos__le_1, cls_le__divide__eq__number__of_2, cls_real__mult__left__cancel_0, cls_abs__ge__zero_0, cls_less__divide__eq_8, cls_divide__le__eq_0, cls_zero__less__divide__iff_3, cls_le__divide__eq__number__of_8, cls_add__num__frac_0, cls_divide__le__eq__number__of1_2, cls_zero__le__divide__iff_4, cls_le__add__iff2_1, cls_double__add__le__zero__iff__single__add__le__zero_0, cls_cos__2npi_0, cls_real__sqrt__ge__one_0, cls_abs__eq__mult_3, cls_real__mult__right__cancel_0, clsarity_RealDef__Oreal__OrderedGroup_Opordered__ab__semigroup__add, cls_pi__half__less__two_0, cls_less__1__mult_0, cls_divide__less__eq__number__of1_9, clsarity_RealDef__Oreal__OrderedGroup_Ocomm__monoid__mult, cls_divide__nonneg__pos_0, cls_arctan__monotone_H_0, cls_mult__less__cancel__right__disj_5, cls_sin__zero_0, cls_divide__le__0__iff_5, cls_linorder__not__le_1, cls_add__less__cancel__right_0, cls_divide__zero_0, cls_minus__less__iff_0, cls_divide__less__eq__number__of_4, cls_add__diff__cancel_0, cls_real__sqrt__gt__zero_0, cls_abs__ge__self_0, cls_tan__pi_0, cls_class__semiring_Omul__a_0, cls_not__less__iff__gr__or__eq_1, cls_neg__0__equal__iff__equal_1, cls_le__add__iff1_0, cls_less__eq__neg__nonpos_1, 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, cls_real__abs__def_1, cls_class__ringb_Oadd__scale__eq__noteq_0, cls_rel__simps_I50_J_0, cls_eq__divide__eq__number__of1_2, cls_real__sqrt__less__iff_0, cls_divide__le__eq_4, cls_pi__half__ge__zero_0, clsarity_nat__Orderings_Opreorder, cls_zero__le__square_0, cls_arctan_2, clsarity_nat__Int_Onumber, cls_order__le__neq__trans_0, cls_divide__less__eq__number__of1_3, cls_class__semiring_Omul__1_0, cls_zero__le__double__add__iff__zero__le__single__add_0, cls_less__divide__eq_1, cls_real__average__minus__first_0, 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clsarity_RealDef__Oreal__Ring__and__Field_Ofield, cls_real__sqrt__one_0, cls_eq__divide__eq__number__of_2, cls_neg__0__less__iff__less_1, cls_zero__le__mult__iff_1, cls_divide__eq__imp_0, cls_minus__mult__left_0, cls_divide__eq__eq__number__of1_4, cls_xt1_I11_J_0, cls_abs__divide_0, cls_pi__neq__zero_0, cls_minus__divide__left_0, cls_sin__double_0, cls_eq__diff__eq_H_0, clsarity_RealDef__Oreal__RealVector_Oreal__normed__field, cls_real__sqrt__gt__1__iff_0, cls_number__of__Bit0_0, cls_real__0__le__add__iff_0, cls_cos__zero_0, cls_le__eqI_0, cls_cos__sin__eq_0, cls_mult__le__cancel__left__neg_0, cls_zero__less__abs__iff_1, cls_divide__less__eq_7, cls_divide__less__eq__number__of_8, cls_abs__if__lattice_1, cls_zero__le__divide__iff_0, cls_cos__gt__zero_0, cls_sin__cos__between__zero__two__pi_0, cls_add__neg__neg_0, cls_mult__imp__div__pos__less_0, cls_tan__total__pi4_0, cls_abs__triangle__ineq_0, cls_double__eq__0__iff_0, cls_one__neq__zero_0, cls_less__divide__eq__number__of1_4, cls_mult__le__0__iff_2, cls_class__semiring_Osemiring__rules_I18_J_0, cls_mult__right__le__one__le_0, cls_real__0__le__divide__iff_2, cls_add__minus__cancel_0, cls_real__le__antisym_0, clsarity_nat__OrderedGroup_Opordered__ab__semigroup__add, cls_sin__periodic__pi__diff_0, cls_mult__1_0, cls_mult_Oadd__right_0, cls_divide__less__0__iff_5, clsarity_RealDef__Oreal__Ring__and__Field_Osemiring, cls_divide__less__eq__number__of_3, cls_neg__less__0__iff__less_1, cls_cos__ge__zero_0, cls_comm__monoid__add_Omult__left__commute_0, cls_add__frac__num_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_le__divide__eq__number__of1_3, cls_diff__divide__distrib_0, cls_cos__periodic__pi_0, cls_divide__less__0__iff_2, cls_diff__0__right_0, cls_xt1_I6_J_0, cls_le__add__right__mono_0, cls_minus__mult__right_0, cls_mult__less__cancel__left__disj_3, cls_divide__le__eq__number__of1_1, 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cls_abs__number__of_0, cls_cos__monotone__0__pi_0, cls_linorder__not__le_0, cls_arctan_1, cls_real__sqrt__eq__1__iff_0, cls_sin__cos__eq_0, cls_less__eq__neg__nonpos_0, cls_le__divide__eq_9, cls_real__add__mult__distrib_0, cls_order__less__irrefl_0, clsarity_nat__Ring__and__Field_Opordered__semiring, cls_add__nonneg__eq__0__iff_2, cls_le__divide__eq_4, cls_class__semiring_Oadd__c_0, cls_sin__monotone__2pi_H_0, cls_less__divide__eq_6, cls_divide__le__eq__number__of1_8, cls_rel__simps_I44_J_0, cls_neg__0__equal__iff__equal_0, cls_mult__left__le__imp__le_0, cls_neg__le__iff__le_0, cls_real__sum__squares__cancel2_0, cls_real__sqrt__gt__0__iff_0, cls_less__minus__self__iff_1, cls_divide__less__0__iff_1, cls_frac__less2_0, clsarity_nat__OrderedGroup_Ocancel__ab__semigroup__add, cls_gt__half__sum_0, cls_divide__less__eq__number__of_9, cls_divide__le__eq__number__of1_3, cls_real__mult__1_0, cls_eq__eqI_1, cls_diff__frac__eq_0, cls_mult__pos__pos_0, cls_less__eqI_0, 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cls_divide__less__eq_9, cls_add__neg__nonpos_0, cls_eq__divide__eq__number__of1_0, cls_mult__divide__mult__cancel__right_0, cls_abs__le__zero__iff_1, cls_class__semiring_Osemiring__rules_I24_J_0, cls_divide__le__eq_9, cls_eq__iff__diff__eq__0_1, cls_add__less__cancel__left_0, cls_class__ringb_Osubr0__iff_1, cls_divide__strict__right__mono_0, cls_abs__one_0, cls_right__minus_0, cls_divide__less__eq_6, cls_real__0__le__divide__iff_1, cls_mult__less__cancel__left__disj_2, cls_minus__add_0, cls_frac__less_0, cls_real__mult__commute_0, clsarity_RealDef__Oreal__OrderedGroup_Omonoid__mult, cls_real__mult__le__cancel__iff1_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_nonzero__minus__divide__divide_0, cls_tan__monotone_0, cls_class__semiring_Osemiring__rules_I25_J_0, cls_less__divide__eq__number__of1_9, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__semiring, clsarity_RealDef__Oreal__OrderedGroup_Olordered__ab__group__add, cls_lemma__real__divide__sqrt__less_0, cls_sin__npi2_0, cls_less__divide__eq_0, clsarity_RealDef__Oreal__Ring__and__Field_Opordered__ring, cls_divide__less__eq__number__of_2, cls_real__less__def_2, cls_add__tan__eq_0, cls_cos__pi__half_0, cls_divide__eq__eq__number__of_2, cls_sin__periodic_0, cls_eq__divide__eq__number__of_0, cls_le__eqI_1, cls_mult__eq__0__iff_1, cls_cos__zero__lemma_0, cls_le__iff__diff__le__0_1, cls_divide__nonpos__pos_0, cls_add__less__le__mono_0, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semidom, cls_divide__less__eq_3, cls_abs__real__of__nat__cancel_0, cls_order__less__imp__le_0, cls_abs__le__D1_0, cls_le__divide__eq__number__of1_4, 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_tan__npi_0, cls_real__le__eq__diff_0, cls_less__divide__eq__number__of_5, cls_le__divide__eq__number__of_4, cls_zero__le__divide__iff_1, cls_sin__3over2__pi_0, cls_cos__two__less__zero_0, cls_tan__gt__zero_0, cls_divide__less__eq__number__of1_1, clsarity_nat__OrderedGroup_Ocomm__monoid__add, cls_eq__iff__diff__eq__0_0, cls_mult__idem_0, cls_monoid__add__class_Oadd__0__right_0, cls_real__sqrt__lt__0__iff_0, cls_sin__diff2_0, cls_cos__add_0, cls_add__strict__increasing2_0, clsarity_RealDef__Oreal__Int_Onumber__ring, cls_divide__eq__eq_1, cls_le__divide__eq_5, cls_real__0__le__divide__iff_5, cls_class__ringb_Osubr0__iff_0, cls_divide__le__eq__number__of1_0, cls_minus__mult__minus_0, clsarity_nat__Ring__and__Field_Omult__zero, cls_divide_Ominus_0, cls_sin__diff_0, cls_mult__less__le__imp__less_0, cls_mult__divide__mult__cancel__left_0, cls_mult__le__less__imp__less_0, cls_mult__left_Ozero_0, cls_eq__diff__eq_H_1, cls_divide__less__0__1__iff_1, cls_le__divide__eq__number__of1_8, cls_divide__less__eq__number__of_5, cls_less__eqI_1, cls_square__eq__iff_0, cls_zero__less__divide__1__iff_0, clsarity_nat__Orderings_Oorder, cls_order__less__le_1, cls_mult__le__0__iff_3, cls_add__numeral__0__right_0, cls_xt1_I7_J_0, 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, cls_le__add__iff2_0, cls_not__one__le__zero_0, cls_less__divide__eq__number__of1_5, clsarity_RealDef__Oreal__Ring__and__Field_Ono__zero__divisors, cls_add__le__cancel__left_0, clsarity_nat__Ring__and__Field_Oordered__semiring__strict, cls_rel__simps_I48_J_0, cls_zero__le__divide__1__iff_0, cls_less__divide__eq_9, cls_even__less__0__iff_0, cls_le__divide__eq__number__of_0, cls_split__mult__neg__le_1, cls_divide__le__eq_1, cls_neg__less__iff__less_0, cls_tan__60_0, cls_mult__left_Oadd_0, cls_comp__arith_I110_J_0, cls_rel__simps_I46_J_0, cls_divide__le__eq__number__of_3, cls_le__divide__eq__number__of_9, cls_sum__squares__le__zero__iff_0, cls_less__divide__eq__number__of_9, cls_abs__triangle__ineq4_0, cls_real__sqrt__ge__0__iff_0, cls_add__le__cancel__right_0, cls_mult__right_Odiff_0, cls_class__semiring_Osemiring__rules_I13_J_0, cls_mult__strict__left__mono__neg_0, cls_real__sqrt__two__ge__zero_0, 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_divide__less__0__iff_4, cls_Deriv_Oadd__diff__add_0, cls_real__mult__self__sum__ge__zero_0, cls_real__add__less__0__iff_1, cls_class__semiring_Osemiring__rules_I22_J_0, cls_real__sqrt__le__iff_1, clsarity_RealDef__Oreal__Ring__and__Field_Oordered__semiring__strict, cls_le__number__of__eq__not__less_0, cls_right__inverse__eq_1, cls_cos__gt__zero__pi_0, cls_cos__monotone__0__pi_H_0, cls_divide__le__eq__number__of_6, cls_less__divide__eq__number__of1_1, cls_abs__diff__less__iff_0, cls_zero__le__mult__iff_2, cls_divide__le__0__1__iff_0, cls_abs__le__interval__iff_1
% 15.17/4.64  % No. of inferences in proof: 2069
% 15.17/4.64  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 4129 ms resp. 3446 ms w/o parsing
% 16.48/4.96  % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 16.48/4.97  % [INFO] 	 Killing All external provers ... 
%------------------------------------------------------------------------------